Journal articles: 'Algorithme de groupe'

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Bachmeyer, Claude, Ziad Reguiaï, Lucie Peuvrel, Jean-Baptiste Bachet, René-Jean Bensadoun, Marc Ychou, Thierry André, Olivier Bouché, and Brigitte Dréno. "Toxicité cutanée des anti-EGFR (epidermal growth factor receptor) : algorithme thérapeutique du groupe français PROCUR." Bulletin du Cancer 100, no. 5 (May 2013): 417–26. http://dx.doi.org/10.1684/bdc.2013.1735.

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C., Sivakumar Chellappan. "Efficient Group Key Management Using Whale Optimization Algorithm based Elliptic Curve Cryptography for Dynamic Multicast Groups." Journal of Advanced Research in Dynamical and Control Systems 12, SP3 (February 28, 2020): 1078–92. http://dx.doi.org/10.5373/jardcs/v12sp3/20201354.

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EVDOKIMENKOV, Veniamin N., Dmitriy A. KOZOREZ, and Mikhail N. KRASILSHCHIKOV. "Development of pre-flight planning algorithms for the functional-program prototype of a distributed intellectual control system of unmanned flying vehicle groups." INCAS BULLETIN 11, S (August 1, 2019): 75–88. http://dx.doi.org/10.13111/2066-8201.2019.11.s.8.

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In article presents algorithmic for a reconnaissance and combat unmanned flying vehicle (UFV) group pre-flight planning. The algorithms, which we elaborated, includes: algorithm, involved for mission target decision, membership selection. Discussing algorithm is based on analytical probabilistic models, providing evaluation of UAF group efficiency operation, considering UAF reliability as well as on board navigation and weapon facility performances; algorithm of UAF routes at the stages of group motion to meeting point and further movement to target area. Developed algorithm provides definition both direction and velocity of UAF, considering actual environment condition and dangerous of UAF recognition by radar, acoustic or infrared facilities of enemy; algorithms of UAF group operation scheduling at the mission target area.

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MARSHALL, JOSEPH. "COMPUTATIONAL PROBLEMS IN HYPERBOLIC GROUPS." International Journal of Algebra and Computation 15, no. 01 (February 2005): 1–13. http://dx.doi.org/10.1142/s0218196705002086.

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We describe an algorithm due to Eric Swenson for testing quasi-convex subgroups of hyperbolic groups for near malnormality. We go on to discuss some strategies for the practical implementation of this algorithm and consider an example. We then show that the methods of Swenson's algorithm extend to give practical solutions to the conjugacy problem for infinite order elements, and to the normalizer and centralizer problems for subgroups satisfying appropriate conditions. The results are presented here in outline — all the algorithms are described in more detail in the author's PhD thesis (University of Warwick, 2001).

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DUCHAMP, GÉRARD, and JEAN-YVES THIBON. "SIMPLE ORDERINGS FOR FREE PARTIALLY COMMUTATIVE GROUPS." International Journal of Algebra and Computation 02, no. 03 (September 1992): 351–55. http://dx.doi.org/10.1142/s0218196792000219.

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We present a method for ordering free partially commutative groups, leading to a simple comparison algorithm. Résumé: Nous présentons une méthode pour ordonner les groupes partiellement commutatifs libres. Cette méthode conduit a un algorithme de comparaison particulièrement simple.

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EPSTEIN, DAVID B. A., and DEREK F. HOLT. "COMPUTATION IN WORD-HYPERBOLIC GROUPS." International Journal of Algebra and Computation 11, no. 04 (August 2001): 467–87. http://dx.doi.org/10.1142/s0218196701000619.

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We describe two practical algorithms for computing with word-hyperbolic groups, both of which we have implemented. The first is a method for estimating the maximum width, if it exists, of geodesic bigons in the Cayley graph of a finitely presented group G. Our procedure will terminate if and only this maximum width exists, and it has been proved by Papasoglu that this is the case if and only if G is word-hyperbolic. So the algorithm amounts to a method of verifying the property of word-hyperbolicity of G. The aim of the second algorithm is to compute the thinness constant for geodesic triangles in the Cayley graph of G. This seems to be a much more difficult problem, but our implementation does succeed with straightforward examples. Both algorithms involve substantial computations with finite state automata.

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Sadeghi, Ali, Sajjad Amiri Doumari, Mohammad Dehghani, Zeinab Montazeri, Pavel Trojovský, and Hamid Jafarabadi Ashtiani. "A New “Good and Bad Groups-Based Optimizer” for Solving Various Optimization Problems." Applied Sciences 11, no. 10 (May 12, 2021): 4382. http://dx.doi.org/10.3390/app11104382.

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Optimization is the science that presents a solution among the available solutions considering an optimization problem’s limitations. Optimization algorithms have been introduced as efficient tools for solving optimization problems. These algorithms are designed based on various natural phenomena, behavior, the lifestyle of living beings, physical laws, rules of games, etc. In this paper, a new optimization algorithm called the good and bad groups-based optimizer (GBGBO) is introduced to solve various optimization problems. In GBGBO, population members update under the influence of two groups named the good group and the bad group. The good group consists of a certain number of the population members with better fitness function than other members and the bad group consists of a number of the population members with worse fitness function than other members of the population. GBGBO is mathematically modeled and its performance in solving optimization problems was tested on a set of twenty-three different objective functions. In addition, for further analysis, the results obtained from the proposed algorithm were compared with eight optimization algorithms: genetic algorithm (GA), particle swarm optimization (PSO), gravitational search algorithm (GSA), teaching–learning-based optimization (TLBO), gray wolf optimizer (GWO), and the whale optimization algorithm (WOA), tunicate swarm algorithm (TSA), and marine predators algorithm (MPA). The results show that the proposed GBGBO algorithm has a good ability to solve various optimization problems and is more competitive than other similar algorithms.

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Grunewald, Fritz, and Daniel Segal. "Decision problems concerning S-arithmetic groups." Journal of Symbolic Logic 50, no. 3 (September 1985): 743–72. http://dx.doi.org/10.2307/2274327.

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This paper is a continuation of our previous work in [12]. The results, and some applications, have been described in the announcement [13]; it may be useful to discuss here, a little more fully, the nature and purpose of this work.We are concerned basically with three kinds of algorithmic problem: (1) isomorphism problems, (2) “orbit problems”, and (3) “effective generation”.(1) Isomorphism problems. Here we have a class of algebraic objects of some kind, and ask: is there a uniform algorithm for deciding whether two arbitrary members of are isomorphic? In most cases, the answer is no: no such algorithm exists. Indeed this has been one of the most notable applications of methods of mathematical logic in algebra (see [26, Chapter IV, §4] for the case where is the class of all finitely presented groups). It turns out, however, that when consists of objects which are in a certain sense “finite-dimensional”, then the isomorphism problem is indeed algorithmically soluble. We gave such algorithms in [12] for the following cases: = {finitely generated nilpotent groups}; = {(not necessarily associative) rings whose additive group is finitely generated}; = {finitely Z-generated modules over a fixed finitely generated ring}.Combining the methods of [12] with his own earlier work, Sarkisian has obtained analogous results with the integers replaced by the rationals: in [20] and [21] he solves the isomorphism problem for radicable torsion-free nilpotent groups of finite rank and for finite-dimensional Q-algebras.

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Wang, Jing, Huafei Sun, and Simone Fiori. "Empirical Means on Pseudo-Orthogonal Groups." Mathematics 7, no. 10 (October 11, 2019): 940. http://dx.doi.org/10.3390/math7100940.

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The present article studies the problem of computing empirical means on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance between two pseudo-orthogonal matrices, which is an essential ingredient, is computed by both the Frobenius norm and the geodesic distance. The empirical-mean computation problem is solved via a pseudo-Riemannian-gradient-stepping algorithm. Several numerical tests are conducted to illustrate the numerical behavior of the devised algorithm.

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Barker, Nathan, Andrew J. Duncan, and David M. Robertson. "The power conjugacy problem in Higman–Thompson groups." International Journal of Algebra and Computation 26, no. 02 (March 2016): 309–74. http://dx.doi.org/10.1142/s0218196716500144.

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An introduction to the universal algebra approach to Higman–Thompson groups (including Thompson’s group [Formula: see text]) is given, following a series of lectures by Graham Higman in 1973. In these talks, Higman outlined an algorithm for the conjugacy problem; which although essentially correct fails in certain cases, as we show here. A revised and complete version of the algorithm is written out explicitly. From this, we construct an algorithm for the power conjugacy problem in these groups. Python implementations of these algorithms can be found in [26].

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Bley, Werner, and Stephen M. J. Wilson. "Computations in Relative Algebraic K-Groups." LMS Journal of Computation and Mathematics 12 (2009): 166–94. http://dx.doi.org/10.1112/s1461157000001480.

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Let G be finite group and K a number field or a p-adic field with ring of integers OK. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K0(OK[G], K) as an abstract abelian group. We also give algorithms to solve the discrete logarithm problems in K0(OK[G], K) and in the locally free class group cl(OK[G]). All algorithms have been implemented in Magma for the case K = Q.In the second part of the manuscript we prove formulae for the torsion subgroup of K0(Z[G], Q) for large classes of dihedral and quaternion groups.

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Popovic, Nashira, Qiuying Yang, and Chris Archibald. "Tendances d’utilisation de la prophylaxie pré-exposition pour le VIH dans huit provinces canadiennes, 2014 à 2018." Relevé des maladies transmissibles au Canada 47, no. 56 (June 9, 2021): 275–83. http://dx.doi.org/10.14745/ccdr.v47i56a02f.

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Contexte : Le Canada a approuvé les objectifs mondiaux du Programme commun des Nations Unies sur le VIH et le Sida visant à mettre fin à l’épidémie du syndrome d’immunodéficience acquise (sida), notamment en réduisant à zéro les nouvelles infections par le virus de l’immunodéficience humaine (VIH) d’ici à 2030. Compte tenu de l’efficacité de la prophylaxie pré-exposition (PPrE) pour prévenir les nouvelles infections, il est important de mesurer et de rendre compte de l’utilisation de la PPrE afin de contribuer à la planification des programmes et des politiques de prévention du VIH. Méthodes : Les estimations annuelles des personnes utilisant de la PPrE au Canada ont été générées pour la période de 2014 à 2018 à partir de l’ensemble de données géographiques de surveillance des ordonnances d’IQVIA. On a utilisé un algorithme pour distinguer les utilisateurs de fumarate de ténofovir disoproxil/emtricitabine (TDF/FTC) pour la PPrE de ceux qui l’utilisent dans le cadre d’un traitement ou de la prophylaxie post-exposition. Nous fournissons le nombre estimé de personnes qui utilisent la PPrE dans huit provinces canadiennes par sexe, groupe d’âge, spécialité du médecin prescripteur et type de paiement. Résultats : Le nombre estimé d’utilisateurs de PPrE a augmenté de façon spectaculaire au cours de la période d’étude de cinq ans : il est multiplié par 21, passant de 460 en 2014 à 9 657 en 2018. La prévalence estimée de la PPrE était de 416 utilisateurs par million de personnes dans les huit provinces en 2018. Presque tous les utilisateurs de PPrE étaient des hommes. L’utilisation a augmenté chez les deux sexes, mais l’augmentation a été plus importante chez les hommes (par 23 fois) que chez les femmes (par 5 fois). L’utilisation a augmenté dans toutes les provinces, bien qu’il y ait des différences entre les provinces relativement à la prévalence de l’utilisation, à la répartition par âge et aux types de médecins prescripteurs. Conclusion : L’utilisation de la PPrE au Canada a augmenté entre 2014 et 2018, ce qui témoigne d’une meilleure connaissance et d’une plus grande adhésion à son utilisation pour prévenir la transmission du VIH. Elle est toutefois inégale en fonction de l’âge, du sexe et de la géographie. Puisque les nouvelles infections au VIH continuent de se produire au Canada, il sera important d’affiner l’utilisation de la PPrE, car les populations à risque plus élevé d’infection au VIH doivent se voir offrir la PPrE dans le cadre de soins de santé sexuelle complets.

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Roman’kov, V. A. "Algorithmic theory of solvable groups." Prikladnaya Diskretnaya Matematika, no. 52 (2021): 16–64. http://dx.doi.org/10.17223/20710410/52/2.

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The purpose of this survey is to give some picture of what is known about algorithmic and decision problems in the theory of solvable groups. We will provide a number of references to various results, which are presented without proof. Naturally, the choice of the material reported on reflects the author’s interests and many worthy contributions to the field will unfortunately go without mentioning. In addition to achievements in solving classical algorithmic problems, the survey presents results on other issues. Attention is paid to various aspects of modern theory related to the complexity of algorithms, their practical implementation, random choice, asymptotic properties. Results are given on various issues related to mathematical logic and model theory. In particular, a special section of the survey is devoted to elementary and universal theories of solvable groups. Special attention is paid to algorithmic questions regarding rational subsets of groups. Results on algorithmic problems related to homomorphisms, automorphisms, and endomorphisms of groups are presented in sufficient detail.

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Leedham-Green, C. R., and E. A. O'Brien. "Recognising Tensor Products of Matrix Groups." International Journal of Algebra and Computation 07, no. 05 (October 1997): 541–59. http://dx.doi.org/10.1142/s0218196797000241.

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As a contribution to the project for recognising matrix groups defined over finite fields, we describe an algorithm for deciding whether or not the natural module for such a matrix group can be decomposed into a non-trivial tensor product. In the affirmative case, a tensor decomposition is returned. As one component, we develop algorithms to compute p-local subgroups of a matrix group.

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Svaba, Pavol, Tran van Trung, and Paul Wolf. "LOGARITHMIC SIGNATURES FOR ABELIAN GROUPS AND THEIR FACTORIZATION." Tatra Mountains Mathematical Publications 57, no. 1 (November 1, 2013): 21–33. http://dx.doi.org/10.2478/tmmp-2013-0033.

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ABSTRACT Factorizable logarithmic signatures for finite groups are the essential component of the cryptosystems MST1 and MST3. The problem of finding efficient algorithms for factoring group elements with respect to a given class of logarithmic signatures is therefore of vital importance in the investigation of these cryptosystems. In this paper we are concerned about the factorization algorithms with respect to transversal and fused transversal logarithmic signatures for finite abelian groups. More precisely we present algorithms and their complexity for factoring group elements with respect to these classes of logarithmic signatures. In particular, we show a factoring algorithm with respect to the class of fused transversal logarithmic signatures and also its complexity based on an idea of Blackburn, Cid and Mullan for finite abelian groups.

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Haas, R., and A. G. Helminck. "Algorithms for Twisted Involutions in Weyl Groups." Algebra Colloquium 19, no. 02 (May 3, 2012): 263–82. http://dx.doi.org/10.1142/s100538671200017x.

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Let (W, Σ) be a finite Coxeter system, and θ an involution such that θ (Δ) = Δ, where Δ is a basis for the root system Φ associated with W, and [Formula: see text] the set of θ-twisted involutions in W. The elements of [Formula: see text] can be characterized by sequences in Σ which induce an ordering called the Richardson-Spinger Bruhat poset. The main algorithm of this paper computes this poset. Algorithms for finding conjugacy classes, the closure of an element and special cases are also given. A basic analysis of the complexity of the main algorithm and its variations is discussed, as well experience with implementation.

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ROGOV, SERGEY I., KUVAT T. MOMYNALIEV, and VADIM M. GOVORUN. "COEXPRESSIONFINDER: A NEW ALGORITHM FOR FINDING GROUPS OF COEXPRESSED GENES." Journal of Bioinformatics and Computational Biology 04, no. 04 (August 2006): 853–64. http://dx.doi.org/10.1142/s0219720006002193.

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Results: A new algorithm is developed which is intended to find groups of genes whose expression values change in a concordant manner in a series of experiments with DNA arrays. This algorithm is named as CoexpressionFinder. It can find more complete and internally coordinated groups of gene expression vectors than hierarchical clustering. Also, it finds more genes having coordinated expression. The algorithm's design allows parallel execution. Availability: The algorithm is implemented as a Java application which is freely available at: and .

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Kumar, G. Vijay, and A. Krishna Chaitanya. "Organizing User Search Histories into Relevant Query Groups by Using Em – Algorithm." Paripex - Indian Journal Of Research 2, no. 2 (January 15, 2012): 116–18. http://dx.doi.org/10.15373/22501991/feb2013/39.

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KARAGIORGOS, GREGORY, and DIMITRIOS POULAKIS. "EFFICIENT ALGORITHMS FOR THE BASIS OF FINITE ABELIAN GROUPS." Discrete Mathematics, Algorithms and Applications 03, no. 04 (December 2011): 537–52. http://dx.doi.org/10.1142/s1793830911001401.

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In this paper we consider the problem of computation of a basis for an abelian group G with N elements such that the prime factorization of N is known. We present two deterministic algorithms for this task and a deterministic algorithm in case where a generating system for G is given.

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Minchenko, Andrei, and Alexey Ovchinnikov. "Calculating Galois groups of third-order linear differential equations with parameters." Communications in Contemporary Mathematics 20, no. 04 (May 20, 2018): 1750038. http://dx.doi.org/10.1142/s0219199717500389.

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Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a parameterized differential Galois group have been recently developed. Extensions of Bessel’s equation, such as the Lommel equation, can be viewed as homogeneous parameterized linear differential equations of the third order. In this paper, we give the first known algorithm that calculates the differential Galois group of a third-order parameterized linear differential equation.

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Nasrinpour, Hamid, Amir Bavani, and Mohammad Teshnehlab. "Grouped Bees Algorithm: A Grouped Version of the Bees Algorithm." Computers 6, no. 1 (January 28, 2017): 5. http://dx.doi.org/10.3390/computers6010005.

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Detinko, A. "On Deciding Finiteness for Matrix Groups over Fields of Positive Characteristic." LMS Journal of Computation and Mathematics 4 (2001): 64–72. http://dx.doi.org/10.1112/s1461157000000802.

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AbstractThe author considers the development of algorithms for deciding whether a finitely generated matrix group over a field of positive characteristic is finite. A deterministic algorithm for deciding the finiteness is presented for the case of a field of transcendence degree one over a finite field.

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Gonçalves, Demerson Nunes, Tharso D. Fernandes, and C. M. M. Cosme. "An Efficient Quantum Algorithm for the Hidden Subgroup Problem over some Non-Abelian Groups." TEMA (São Carlos) 18, no. 2 (August 24, 2017): 0215. http://dx.doi.org/10.5540/tema.2017.018.02.0215.

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The hidden subgroup problem (HSP) plays an important role in quantum computation, because many quantum algorithms that are exponentially faster than classical algorithms are special cases of the HSP. In this paper we show that there exist a new efficient quantum algorithm for the HSP on groups $\Z_{N}\rtimes\Z_{q^s}$ where $N$ is an integer with a special prime factorization, $q$ prime number and $s$ any positive integer.

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MARKUS-EPSTEIN, L. "STALLINGS FOLDINGS AND SUBGROUPS OF AMALGAMS OF FINITE GROUPS." International Journal of Algebra and Computation 17, no. 08 (December 2007): 1493–535. http://dx.doi.org/10.1142/s0218196707003846.

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Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse automaton. This allows for the deep algorithmic theory of finite automata and finite inverse monoids to be used to answer questions about finitely generated subgroups of free groups. In this paper, we attempt to apply the same methods to other classes of groups. A fundamental new problem is that the Stallings folding algorithm must be modified to allow for "sewing" on relations of non-free groups. We look at the class of groups that are amalgams of finite groups. It is known that these groups are locally quasiconvex and thus, all finitely generated subgroups are represented by finite automata. We present an algorithm to compute such a finite automaton and use it to solve various algorithmic problems.

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HOLT, DEREK F., SARAH REES, and MICHAEL SHAPIRO. "GROUPS THAT DO AND DO NOT HAVE GROWING CONTEXT-SENSITIVE WORD PROBLEM." International Journal of Algebra and Computation 18, no. 07 (November 2008): 1179–91. http://dx.doi.org/10.1142/s0218196708004834.

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We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and Shapiro in [6]). We generalize results of [6] to find many examples of groups not admitting non-deterministic Cannon's algorithms. This adds to the examples of Kambites and Otto in [7] of groups separating context-sensitive and growing context-sensitive word problems, and provides a new language-theoretic separation result.

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Mecky, M., and J. Neubüser. "Some remarks on the computation of conjugacy classes of soluble groups." Bulletin of the Australian Mathematical Society 40, no. 2 (October 1989): 281–92. http://dx.doi.org/10.1017/s0004972700004378.

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Laue et al have described basic algorithms for computing in a finite soluble group G given by an AG-presentation, among them a general algorithm for the computation of the orbits of such a group acting on some set Ω. Among other applications, this algorithm yields straightforwardly a method for the computation of the conjugacy classes of elements in such a group, which has been implemented in 1986 in FORTRAN within SOGOS by the first author and in 1987 in C within CAYLEY. However, for this particular problem one can do better, as discussed in this note.

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Ambrose, Sophie, Max Neunhöffer, Cheryl E. Praeger, and Csaba Schneider. "Generalised Sifting in Black-Box Groups." LMS Journal of Computation and Mathematics 8 (2005): 217–50. http://dx.doi.org/10.1112/s1461157000000978.

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AbstractThis paper presents a generalisation of the sifting procedure introduced originally by Sims for computation with finite permutation groups, and now used for many computational procedures for groups, such as membership testing and finding group orders. The new procedure is a Monte Carlo algorithm, and it is presented and analysed in the context of black-box groups. It is based on a chain of subsets instead of a subgroup chain. Two general versions of the procedure are worked out in detail, and applications are given for membership tests for several of the sporadic simple groups. The authors' major objective was that the procedures could be proved to be Monte Carlo algorithms, and the costs computed. In addition, they explicitly determined suitable subset chains for six of the sporadic groups, and then implemented the algorithms involving these chains in the GAP computational algebra system. It turns out that sample imple-mentations perform well in practice. The implementations will be made available publicly in the form of a GAP package.

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Eick, Bettina, and Bernd Souvignier. "Algorithms for crystallographic groups." International Journal of Quantum Chemistry 106, no. 1 (2005): 316–43. http://dx.doi.org/10.1002/qua.20747.

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AlShabi, Mohammad, Chaouki Ghenai, Maamar Bettayeb, and Fahad Faraz Ahmad. "Estimating one-diode-PV model using autonomous groups particle swarm optimization." IAES International Journal of Artificial Intelligence (IJ-AI) 10, no. 1 (March 1, 2021): 166. http://dx.doi.org/10.11591/ijai.v10.i1.pp166-174.

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In this paper, the one-diode model of a photovoltaic PV solar cell (PVSC) is estimated for an experimental characteristic curves data by using a recently proposed version of the Particle Swarm Optimization (PSO) algorithm, which is known as the Autonomous Groups Particles Swarm Optimization (PSOAG). This meta-heuristic algorithm is used to identify the model of the PVSC. The PSOAG divides the particles into groups and then, uses different functions to tune the social and cognitive parameters of these groups. This is done to show the individuals’ diversity inside the swarm. Although, these individuals do their duties as part of the society, they are not similar in terms of intelligence and ability. By using these groups, the performance of the PSO is improved in terms of convergence rate and escaping the local minima/maxima. Six versions of PSOAG algorithms were developed in this work. Therefore, nine versions of PSOAG, including these six algorithms and three newly developed PSOAG reported previously, will be used in this research to cover more social’s behaviors. The results are compared to the original PSO and other versions of PSO like conventional and Asymmetric Time-varying Accelerated Coefficient PSOs, and the improved PSO. The result shows that the proposed methods improve the performance by up to 14% in terms of root mean squared error and maximum absolute error, and by up to 20% in term of convergence rate, when these were compared to the best results obtained from the other algorithms.

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Gupta, Medha, and Divya Gupta. "A New Modified Firefly Algorithm." International Journal of Recent Contributions from Engineering, Science & IT (iJES) 4, no. 2 (July 5, 2016): 18. http://dx.doi.org/10.3991/ijes.v4i2.5879.

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Nature inspired meta-heuristic algorithms studies the emergent collective intelligence of groups of simple agents. Firefly Algorithm is one of the new such swarm-based metaheuristic algorithm inspired by the flashing behavior of fireflies. The algorithm was first proposed in 2008 and since then has been successfully used for solving various optimization problems. In this work, we intend to propose a new modified version of Firefly algorithm (MoFA) and later its performance is compared with the standard firefly algorithm along with various other meta-heuristic algorithms. Numerical studies and results demonstrate that the proposed algorithm is superior to existing algorithms.

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Virmani, Deepali, Nikita Jain, Ketan Parikh, Shefali Upadhyaya, and Abhishek Srivastav. "Proficient Normalised Fuzzy K-Means With Initial Centroids Methodology." International Journal of Knowledge Discovery in Bioinformatics 8, no. 1 (January 2018): 42–59. http://dx.doi.org/10.4018/ijkdb.2018010104.

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This article describes how data is relevant and if it can be organized, linked with other data and grouped into a cluster. Clustering is the process of organizing a given set of objects into a set of disjoint groups called clusters. There are a number of clustering algorithms like k-means, k-medoids, normalized k-means, etc. So, the focus remains on efficiency and accuracy of algorithms. The focus is also on the time it takes for clustering and reducing overlapping between clusters. K-means is one of the simplest unsupervised learning algorithms that solves the well-known clustering problem. The k-means algorithm partitions data into K clusters and the centroids are randomly chosen resulting numeric values prohibits it from being used to cluster real world data containing categorical values. Poor selection of initial centroids can result in poor clustering. This article deals with a proposed algorithm which is a variant of k-means with some modifications resulting in better clustering, reduced overlapping and lesser time required for clustering by selecting initial centres in k-means and normalizing the data.

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Luckyana, Nabila Divanadia, Ahmad Afif Supianto, and Tibyani Tibyani. "Implementasi Kombinasi Algoritme Self-Organizing Map dan Fuzzy C-Means untuk Pengelompokan Performa Belajar Siswa pada Media Pembelajaran Digital." Jurnal Teknologi Informasi dan Ilmu Komputer 8, no. 3 (June 15, 2021): 549. http://dx.doi.org/10.25126/jtiik.2021834402.

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Media pembelajaran digital mampu menyimpan data dalam bentuk log data yang dapat digunakan untuk melihat perbedaan performa siswa yang tentu saja berbeda-beda antara satu siswa dengan siswa yang lainnya. Perbedaan performa siswa tersebut menyebabkan dibutuhkannya sebuah tahapan yang berfungsi untuk mempermudah proses evaluasi dengan cara menempatkan siswa kedalam kelompok yang sesuai agar dapat membantu tenaga pengajar dalam menangani serta memberikan umpan balik yang tepat pada siswanya. Penelitian ini bertujuan memanfaatkan log data dari sebuah media pembelajaran digital dengan menggunakan kombinasi dari algoritme Self-Organizing Map dan Fuzzy C-Means untuk mengelompokan siswa berdasarkan aktivitas mereka selama belajar dengan media tersebut. Data akan melalui sebuah proses reduksi dimensi dengan menggunakan algoritme SOM, lalu dikelompokkan dengan menggunakan algoritme FCM. Selanjutnya, data dievaluasi dengan menggunakan nilai silhouette coefficient dan dibandingkan dengan algoritme SOM clustering konvensional. Berdasarkan hasil implementasi yang telah dilakukan menggunakan 12 data assignment pada media pembelajaran Monsakun, dihasilkan parameter-parameter optimal seperti ukuran map atau jumlah output neuron sejumlah 25x25 dengan nilai learning rate yang berbeda-beda disetiap assignment. Selain itu, diperoleh pula 2 kelompok siswa pada setiap assignment berdasarkan nilai silhouette coefficient tertinggi yang mencapai lebih dari 0.8 di beberapa assignment. Melalui serangkaian pengujian yang telah dilakukan, penerapan kombinasi algoritme SOM dan FCM secara signifikan menghasilkan cluster yang lebih baik dibandingkan dengan algoritme SOM clustering konvensional. Abstract Digital learning media is able to store data in the form of log data that can be used to see differences in student performance. The difference in student performance causes the need for a stage that functions to simplify the evaluation process by placing students into appropriate groups in order to assist the teaching staff in handling and providing appropriate feedback to students. This study aims to utilize log data from a digital learning media using a combination of the Self-Organizing Map algorithm and Fuzzy C-Means to classify students based on their activities while learning with these media. The data will go through a dimensional reduction process using the SOM algorithm, then grouped using the FCM algorithm. Furthermore, the data were evaluated using the silhouette coefficient value and compared with the conventional SOM clustering algorithm. Based on the results of the implementation that has been carried out using 12 data assignments on the Monsakun learning media, optimal parameters such as map size or the number of neuron outputs are 25x25 with different learning rate values in each assignment. In addition, 2 groups of students were obtained for each assignment based on the highest silhouette coefficient score which reached more than 0.8 in several assignments. Through a series of tests that have been carried out, the implementation of a combination of the SOM and FCM algorithms has significantly better clusters than the conventional SOM clustering algorithm.

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Adraoui, Meriem, Asmaâ Retbi, Mohammed Khalidi Idrissi, and Samir Bennani. "A New Algorithm to Detect and Evaluate Learning Communities in Social Networks: Facebook Groups." International Journal of Emerging Technologies in Learning (iJET) 14, no. 23 (December 6, 2019): 165. http://dx.doi.org/10.3991/ijet.v14i23.10889.

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This article aims to present a new method of evaluating learners by communities on Facebook groups which based on their interactions. The objective of our study is to set up a community learning structure according to the learners' levels. In this context, we have proposed a new algorithm to detect and evaluate learning communities. Our algorithm consists of two phases. The first phase aims to evaluate learners by measuring their degrees of ‘Safely’. The second phase is used to detect communities. These two phases will be repeated until the best community structure is found. Finally, we test the performance of our proposed approach on five Facebook groups. Our algorithm gives good results compared to other community detection algorithms.

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Parivash, Ranjbar. "Signal Processing Methods for Improvement of Environmental Perception of Persons with Deafblindness." Advanced Materials Research 902 (February 2014): 398–404. http://dx.doi.org/10.4028/www.scientific.net/amr.902.398.

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Environmental perception is a functional area that is severely limited in persons with deafblindness (DB) who belong a category of people with severe disabilities. Monitor is a vibratory aid developed with the aim to improve environmental perception of persons with DB. The aid consists of a mobile phone with an application connected to a microphone and vibrator. Monitor picks up the sounds produced by events by microphone, processes the sound using an algorithm programmed as an application in the mobile phone and then presents the signal via the vibrator to the persons with DB to be sensed and interpreted. In previous laboratory studies, four algorithms (AM, AMMC, TR, and TRHA) were developed based on modulating, and transposing principles. The algorithms were tested by persons with normal hearing/hearing impairment and selected as good candidates to improve vibratory identification of environmental sounds. In this on-going the algorithms are tested by 13 persons with congenital D and five persons with DB using Monitor in a realistic environment, living room, kitchen or office. Forty five recorded environmental sounds were used as test stimuli. The subjects tested the algorithms two times, Test and Retest each including a test session initiated by a training session. The four algorithms were tested in four days at Test and four days at Retest in total eight test days. Each test day began with a training session where a sound was presented as vibrations to be sensed by the person with the aim to remember its pattern and identity. The 45 sounds were grouped in four groups where an specific algorithm was chosen to process an specific sound group in a specific day. At the test session a sound was presented and the person was given 5 randomly chosen sound alternatives to choose the one as represented sound. The algorithms were different for different sound groups during four different test days so all algorithms were used to process all sounds. The algorithms were tested a second time, Retest, in same way as in Test. The mean value of identification of environmental sounds varied between 74.6% and 84.0% at Test and between 86.9% and 90.4% at Retest. The identification results at Retest were significantly improved (p<0.01) for all algorithms after a relatively short time of training indicating a good learning effect. At Test the algorithm AM was significantly better than the algorithms AMMC and TRHA (p< 0.01) and the algorithm TR was better than TRHA (p<0.01). The algorithms AM, AMMC, and TR were selected as good candidates to be implemented in the Monitor to improve environmental perception.

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Kopsov, Igor. "Comparison of Algorithms of Individual and Group Behavior." Advances in Social Sciences Research Journal 8, no. 2 (February 28, 2021): 487–510. http://dx.doi.org/10.14738/assrj.82.9750.

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It has been suggested that the functionality of matter, life, and mind can be described by algorithms containing a sequence of steps and feedback mechanisms. Social processes were until now not considered. Consequently, we examine algorithms of behavior of groups of various kinds, identify their common parameters, and undertake a comparative analysis to the algorithm of individual behavior. We conclude, that despite some application-specific differences, groups operate in accordance with a unified algorithm and, furthermore, this algorithm is the same as the generic algorithm of individual behavior. We demonstrate that in the generally perceived progression matter-life-mind-culture/society, the latter transition cannot be validated. Homogeneity of algorithms of individual and group behavior leads to the proposition that the human mind/psyche and social processes belong to the same level of complexity of nature. This challenges the commonly held perception that society/culture is a standalone perspective of reality separate from the mind.

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Opara, Ralf, and Florentin Wörgötter. "A Fast and Robust Cluster Update Algorithm for Image Segmentation in Spin-Lattice Models Without Annealing—Visual Latencies Revisited." Neural Computation 10, no. 6 (August 1, 1998): 1547–66. http://dx.doi.org/10.1162/089976698300017304.

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Image segmentation in spin-lattice models relies on the fast and reliable assignment of correct labels to those groups of spins that represent the same object. Commonly used local spin-update algorithms are slow because in each iteration only a single spin is flipped and a careful annealing schedule has to be designed in order to avoid local minima and correctly label larger areas. Updating of complete spin clusters is more efficient, but often clusters that should represent different objects will be conjoined. In this study, we propose a cluster update algorithm that, similar to most local update algorithms, calculates an energy function and determines the probability for flipping a whole cluster of spins by the energy gain calculated for a neighborhood of the regarded cluster. The novel algorithm, called energy-based cluster update (ECU algorithm) is compared to its predecessors. A convergence proof is derived, and it is shown that the algorithm outperforms local update algorithms by far in speed and reliability. At the same time it is more robust and noise tolerant than other versions of cluster update algorithms, making annealing completely unnecessary. The reduction in computational effort achieved this way allows us to segment real images in about 1–5 sec on a regular workstation. The ECU-algorithm can recover fine details of the images, and it is to a large degree robust with respect to luminance-gradients across objects. In a final step, we introduce luminance dependent visual latencies (Opara & Wörgötter, 1996; Wörgötter, Opara, Funke, & Eysel, 1996) into the spin-lattice model. This step guarantees that only spins representing pixels with similar luminance become activated at the same time. The energy function is then computed only for the interaction of the regarded cluster with the currently active spins. This latency mechanism improves the quality of the image segmentation by another 40%. The results shown are based on the evaluation of gray-level differences. It is important to realize that all algorithmic components can be transferred easily to arbitrary image features, like disparity, texture, and motion.

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Чуканов, Андрей, and Andrey Chukanov. "Clusterization of Russian Regions by the Level of Mortgage Developing." Scientific Research and Development. Economics 7, no. 1 (March 4, 2019): 31–36. http://dx.doi.org/10.12737/article_5c59831d0d88f2.82305663.

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In this article, in order to optimize the economic policy in the field of mortgagehousing lending, the clustering of Russian regions by the most optimal method was carried out and analyzed. The main limitations arising from the application of the most popular k-means clustering algorithm for analyzing mortgages are considered and ways to correct them are suggested. The regions were grouped using clustering algorithms using medians and medoids that are more resistant to outliers. A comparison was made of the results of the k-means, k-medians and k-medoids algorithms, and the optimal number of groups of regions with similar indicators in the field of mortgage lending and their relevant regions representatives were found. A hierarchical clustering algorithm based on the Ward method was used, the result of which was the use of five mortgage clusters in Russia. The study of the characteristics of these groups of regions will help in creating a mortgage policy that takes into account the peculiarities of the regions of Russia. All calculations were made in the R programming language; graphics were created in the Rstudio development environment.

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XUE, Janet Hui. "Algorithmic Vulnerability in Deploying Vaccination Certificates in the European Union and China." European Journal of Risk Regulation 12, no. 2 (June 2021): 332–42. http://dx.doi.org/10.1017/err.2021.32.

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This article further develops the concept of algorithmic vulnerability. The analysis is built on empirical evidence of the Chinese Health Code System (HCS), compared to similar plans for the “COVID-19 Certificate” in the European Union (EU). Implementing the HCS has shown two-sided regulatory implications: improving social protection (a national strategy, a common mutual-recognition standard, scaled-up public–private cooperation) and increasing risks of social exclusion (non-digital and digital forms of vulnerability). This article argues that algorithmic vulnerability is caused by mismatches between biased databases, unfairly pre-designed algorithms and dynamically changed risk groups in reality in the context of COVID-19 vaccination. It contributes a framework for deploying plans for digital certificates in the EU concerning minimising the social risks associated with algorithmic vulnerability. The framework consists of (1) reinforcing existing vulnerability inherited from non-digital society (eg caused by intersectional factors of race/ethnicity, gender, age and health) and (2) introducing new forms of vulnerability generated by algorithm design and implementation (eg excluding the risk groups of individuals who are un/mis/overrepresented in the databases, such as those defined by nationality plus COVID-19 status).

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Galiautdinov, Rinat. "Methods of Information Processing of Relative Motion in the Flying Groups of UAV." International Journal of Software Science and Computational Intelligence 13, no. 1 (January 2021): 90–108. http://dx.doi.org/10.4018/ijssci.2021010106.

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In this article, the author investigates information processing algorithms in order to determine the relative UAV motion parameters in a group flight and proposes an algorithm for estimating the leading UAV motion parameters from the results of relative motion measurements. Such researches are especially important nowadays in all the spheres where the drones are used and/or will be used. The author considers the problems of management of the UAV in the group flight, formulation of the problem for processing of the information in such the conditions. The article considers relative motion equation and the synthesis of information processing algorithms in the master-slave model of the flying group of UAV.

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Yildizdan, Gülnur, and Ömer Kaan Baykan. "A New Hybrid BA_ABC Algorithm for Global Optimization Problems." Mathematics 8, no. 10 (October 12, 2020): 1749. http://dx.doi.org/10.3390/math8101749.

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Bat Algorithm (BA) and Artificial Bee Colony Algorithm (ABC) are frequently used in solving global optimization problems. Many new algorithms in the literature are obtained by modifying these algorithms for both constrained and unconstrained optimization problems or using them in a hybrid manner with different algorithms. Although successful algorithms have been proposed, BA’s performance declines in complex and large-scale problems are still an ongoing problem. The inadequate global search capability of the BA resulting from its algorithm structure is the major cause of this problem. In this study, firstly, inertia weight was added to the speed formula to improve the search capability of the BA. Then, a new algorithm that operates in a hybrid manner with the ABC algorithm, whose diversity and global search capability is stronger than the BA, was proposed. The performance of the proposed algorithm (BA_ABC) was examined in four different test groups, including classic benchmark functions, CEC2005 small-scale test functions, CEC2010 large-scale test functions, and classical engineering design problems. The BA_ABC results were compared with different algorithms in the literature and current versions of the BA for each test group. The results were interpreted with the help of statistical tests. Furthermore, the contribution of BA and ABC algorithms, which constitute the hybrid algorithm, to the solutions is examined. The proposed algorithm has been found to produce successful and acceptable results.

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Meyer, Paul N., Kai Fu, Timothy C. Greiner, Lynette M. Smith, Jan Delabie, Randy D. Gascoyne, German Ott, et al. "Immunohistochemical Methods for Predicting Cell of Origin and Survival in Patients With Diffuse Large B-Cell Lymphoma Treated With Rituximab." Journal of Clinical Oncology 29, no. 2 (January 10, 2011): 200–207. http://dx.doi.org/10.1200/jco.2010.30.0368.

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Purpose Patients with diffuse large B-cell lymphoma (DLBCL) can be divided into prognostic groups based on the cell of origin of the tumor as determined by microarray analysis. Various immunohistochemical algorithms have been developed to replicate these microarray results and/or stratify patients according to survival. This study compares some of those algorithms and also proposes some modifications. Patients and Methods Two-hundred and sixty-two cases of de novo DLBCL treated with rituximab and cyclophosphamide, doxorubicin, vincristine, and prednisone (CHOP) or CHOP-like therapy were examined. Results The Choi algorithm and Hans algorithm had high concordance with the microarray results. Modifications of the Choi and Hans algorithms for ease of use still retained high concordance with the microarray results. Although the Nyman and Muris algorithms had high concordance with the microarray results, each had a low value for either sensitivity or specificity. The use of LMO2 alone showed the lowest concordance with the microarray results. A new algorithm (Tally) using a combination of antibodies, but without regard to the order of examination, showed the greatest concordance with microarray results. All of the algorithms divided patients into groups with significantly different overall and event-free survivals, but with different hazard ratios. With the exception of the Nyman algorithm, this survival prediction was independent of the International Prognostic Index. Although the Muris algorithm had prognostic significance, it misclassified a large number of cases with activated B-cell type DLBCL. Conclusion The Tally algorithm showed the best concordance with the microarray data while maintaining prognostic significance and ease of use.

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JÄNTSCHI, Lorentz, Sorana D. BOLBOACĂ, Mugur C. BĂLAN, Radu E. SESTRAS, and Mircea V. DIUDEA. "Results of Evolution Supervised by Genetic Algorithms." Notulae Scientia Biologicae 2, no. 3 (September 27, 2010): 12–15. http://dx.doi.org/10.15835/nsb234873.

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The efficiency of a genetic algorithm is frequently assessed using a series of operators of evolution like crossover operators, mutation operators or other dynamic parameters. The present paper aimed to review the main results of evolution supervised by genetic algorithms used to identify solutions to agricultural and horticultural hard problems and to discuss the results of using a genetic algorithms on structure-activity relationships in terms of behavior of evolution supervised by genetic algorithms. A genetic algorithm had been developed and implemented in order to identify the optimal solution in term of estimation power of a multiple linear regression approach for structure-activity relationships. Three survival and three selection strategies (proportional, deterministic and tournament) were investigated in order to identify the best survival-selection strategy able to lead to the model with higher estimation power. The Molecular Descriptors Family for structure characterization of a sample of 206 polychlorinated biphenyls with measured octanol-water partition coefficients was used as case study. Evolution using different selection and survival strategies proved to create populations of genotypes living in the evolution space with different diversity and variability. Under a series of criteria of comparisons these populations proved to be grouped and the groups were showed to be statistically different one to each other. The conclusions about genetic algorithm evolution according to a number of criteria were also highlighted.

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GOODMAN, OLIVER, and MICHAEL SHAPIRO. "ON A GENERALIZATION OF DEHN'S ALGORITHM." International Journal of Algebra and Computation 18, no. 07 (November 2008): 1137–77. http://dx.doi.org/10.1142/s0218196708004822.

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Viewing Dehn's algorithm as a rewriting system, we generalize to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to include finitely generated nilpotent groups, many relatively hyperbolic groups including geometrically finite groups and fundamental groups of certain geometrically decomposable 3-manifolds. The class has several nice closure properties. We also show that if a group has an infinite subgroup and one of exponential growth, and they commute, then it does not admit such an algorithm. We dub these Cannon's algorithms.

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Shum, Michael, Max Kleiman-Weiner, Michael L. Littman, and Joshua B. Tenenbaum. "Theory of Minds: Understanding Behavior in Groups through Inverse Planning." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 6163–70. http://dx.doi.org/10.1609/aaai.v33i01.33016163.

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Human social behavior is structured by relationships. We form teams, groups, tribes, and alliances at all scales of human life. These structures guide multi-agent cooperation and competition, but when we observe others these underlying relationships are typically unobservable and hence must be inferred. Humans make these inferences intuitively and flexibly, often making rapid generalizations about the latent relationships that underlie behavior from just sparse and noisy observations. Rapid and accurate inferences are important for determining who to cooperate with, who to compete with, and how to cooperate in order to compete. Towards the goal of building machine-learning algorithms with human-like social intelligence, we develop a generative model of multiagent action understanding based on a novel representation for these latent relationships called Composable Team Hierarchies (CTH). This representation is grounded in the formalism of stochastic games and multi-agent reinforcement learning. We use CTH as a target for Bayesian inference yielding a new algorithm for understanding behavior in groups that can both infer hidden relationships as well as predict future actions for multiple agents interacting together. Our algorithm rapidly recovers an underlying causal model of how agents relate in spatial stochastic games from just a few observations. The patterns of inference made by this algorithm closely correspond with human judgments and the algorithm makes the same rapid generalizations that people do.

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van Kreveld, Marc, Maarten Löffler, Frank Staals, and Lionov Wiratma. "A Refined Definition for Groups of Moving Entities and Its Computation." International Journal of Computational Geometry & Applications 28, no. 02 (June 2018): 181–96. http://dx.doi.org/10.1142/s0218195918600051.

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One of the important tasks in the analysis of spatio-temporal data collected from moving entities is to find a group: a set of entities that travel together for a sufficiently long period of time. Buchin et al.2 introduce a formal definition of groups, analyze its mathematical structure, and present efficient algorithms for computing all maximal groups in a given set of trajectories. In this paper, we refine their definition and argue that our proposed definition corresponds better to human intuition in certain cases, particularly in dense environments. We present algorithms to compute all maximal groups from a set of moving entities according to the new definition. For a set of [Formula: see text] moving entities in [Formula: see text], specified by linear interpolation in a sequence of [Formula: see text] time stamps, we show that all maximal groups can be computed in [Formula: see text] time. A similar approach applies if the time stamps of entities are not the same, at the cost of a small extra factor of [Formula: see text] in the running time, where [Formula: see text] denotes the inverse Ackermann function. In higher dimensions, we can compute all maximal groups in [Formula: see text] time (for any constant number of dimensions), regardless of whether the time stamps of entities are the same or not. We also show that one [Formula: see text] factor can be traded for a much higher dependence on [Formula: see text] by giving a [Formula: see text] algorithm for the same problem. Consequently, we give a linear-time algorithm when the number of entities is constant and the input size relates to the number of time stamps of each entity. Finally, we provide a construction to show that it might be difficult to develop an algorithm with polynomial dependence on [Formula: see text] and linear dependence on [Formula: see text].

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Leschyov, Dmitry, Daniel Suchkov, Svetlana Khaykova, and Alexander Chepovskiy. "Algorithms to Reveal Communication Groups." Voprosy kiberbezopasnosti, no. 4(32) (2019): 61–71. http://dx.doi.org/10.21681/2311-3456-2019-4-61-71.

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Chen, Ke, and Adrian Dumitrescu. "Selection Algorithms with Small Groups." International Journal of Foundations of Computer Science 31, no. 03 (April 2020): 355–69. http://dx.doi.org/10.1142/s0129054120500136.

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We revisit the selection problem, namely that of computing the [Formula: see text]th order statistic of [Formula: see text] given elements, in particular the classic deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973). Whereas the original algorithm uses groups of odd size at least [Formula: see text] and runs in linear time, it has been perpetuated in the literature that using smaller group sizes will force the worst-case running time to become superlinear, namely [Formula: see text]. We first point out that the usual arguments found in the literature justifying the superlinear worst-case running time fall short of proving this claim. We further prove that it is possible to use group size smaller than [Formula: see text] while maintaining the worst case linear running time. To this end we introduce three simple variants of the classic algorithm, the repeated step algorithm, the shifting target algorithm, and the hyperpair algorithm, all running in linear time.

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Figueiredo, Adelaide. "Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions." Open Statistics & Probability Journal 08, no. 1 (December 29, 2017): 39–52. http://dx.doi.org/10.2174/1876527001708010039.

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Background:In the statistical analysis of directional data, the von Mises-Fisher distribution plays an important role to model unit vectors. The estimation of the parameters of a mixture of von Mises-Fisher distributions can be done through the Estimation-Maximization algorithm.Objective:In this paper we propose a dynamic clusters type algorithm based on the estimation of the parameters of a mixture of von Mises-Fisher distributions for clustering directions, and we compare this algorithm with the Estimation-Maximization algorithm. We also define the between-groups and within-groups variability measures to compare the solutions obtained with the algorithms through these measures.Results:The comparison of the clusters obtained with both algorithms is provided for a simulation study based on samples generated from a mixture of two Fisher distributions and for an illustrative example with spherical data.

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Saharidis, Georgios K. D. "Review of Solution Approaches for the Symmetric Traveling Salesman Problem." International Journal of Information Systems and Supply Chain Management 7, no. 1 (January 2014): 73–87. http://dx.doi.org/10.4018/ijisscm.2014010105.

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In this paper, the main known exact and heuristic solution approaches and algorithms for the symmetric Traveling Salesman Problem (TSP), published after 1992, are surveyed. The paper categorize the most important existing algorithm to 6 main groups: i) Genetic algorithms, ii) Ant colony methods, iii) Neural Methods, iv) Local search algorithms and Tabu search, v) Lagrangian methods and vi) Branch and bound and branch & cut algorithms.

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Real, Pedro. "An algorithm computing homotopy groups." Mathematics and Computers in Simulation 42, no. 4-6 (November 1996): 461–65. http://dx.doi.org/10.1016/s0378-4754(96)00021-3.

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Journal articles on the topic 'Algorithme de groupe'

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