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Journal articles on the topic 'Euclidean combinatorial optimization'

Author: Grafiati

Published: 28 May 2022

Last updated: 18 July 2025

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1

Steele, J. Michael. "Probability and Problems in Euclidean Combinatorial Optimization." Statistical Science 8, no. 1 (1993): 48–56. http://dx.doi.org/10.1214/ss/1177011083.

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2

Michael Steele, J. "Efficacy of spacefilling heuristics in Euclidean combinatorial optimization." Operations Research Letters 8, no. 5 (1989): 237–39. http://dx.doi.org/10.1016/0167-6377(89)90046-1.

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3

Moraglio, Alberto, Cecilia Di Chio, Julian Togelius, and Riccardo Poli. "Geometric Particle Swarm Optimization." Journal of Artificial Evolution and Applications 2008 (February 21, 2008): 1–14. http://dx.doi.org/10.1155/2008/143624.

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Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimisation (PSO) and evolutionary algorithms. This connection enables us to generalise PSO to virtually any solution representation in a natural and straightforward way. The new Geometric PSO (GPSO) applies naturally to both continuous and combinatorial spaces. We demonstrate this for the cases of Euclidean, Manhattan and Hamming spaces and report extensive experimental results. We also demonstrate the applicability of GPSO to more challenging combinat

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4

Barbolina, Tetiana. "Estimates of objective function minimum for solving linear fractional unconstrained combinatorial optimization problems on arrangements." Physico-mathematical modelling and informational technologies, no. 32 (July 6, 2021): 32–36. http://dx.doi.org/10.15407/fmmit2021.32.055.

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The paper is devoted to the study of one class of Euclidean combinatorial optimization problems — combinatorial optimization problems on the general set of arrangements with linear fractional objective function and without additional (non-combinatorial) constraints. The paper substantiates the improvement of the polynomial algorithm for solving the specified class of problems. This algorithm foresees solving a finite sequence of linear unconstrained problems of combinatorial optimization on arrangements. The modification of the algorithm is based on the use of estimates of the objective functi

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5

Jaillet, Patrick. "Analysis of Probabilistic Combinatorial Optimization Problems in Euclidean Spaces." Mathematics of Operations Research 18, no. 1 (1993): 51–70. http://dx.doi.org/10.1287/moor.18.1.51.

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6

Barbolina, T. M. "Properties of Euclidean Problems of Lexicographic Combinatorial Optimization on Arrangements." Mathematical and computer modelling. Series: Physical and mathematical sciences, no. 19 (June 25, 2019): 5–11. http://dx.doi.org/10.32626/2308-5878.2019-19.5-11.

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7

Wang, Hongjian, Abdelkhalek Mansouri, and Jean-Charles Créput. "Cellular matrix model for parallel combinatorial optimization algorithms in Euclidean plane." Applied Soft Computing 61 (December 2017): 642–60. http://dx.doi.org/10.1016/j.asoc.2017.08.015.

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8

U., Tormosov, Stoyan E., and Yakushenko E. "THE PROBLEM OF MINIMIZING THE SUMMARY AREA OF MOBILE INTERRUPTIONS AT A LINEAR PLACEMENT OF GEOMETRIC OBJECTS." PROGRESSIVE TECHNIQUE AND TECHNOLOGIES OF FOOD PRODUCTION ENTERPRISES, CATERING BUSINESS AND TRADE 1(29) (June 30, 2019): 239–47. https://doi.org/10.5281/zenodo.3263757.

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<em>The high computational complexity of the combinatorial optimization methods, the difference of the combinatorial properties of the sets which form the ranges of admissible solutions, are the reasons for the lack of unified approach to combinatorial optimization problems solving. The basic idea of the combinatorial methods consists in the transition from complete enumeration of finite set of solutions to reduced one. The impossibility of exact solution of combinatorial optimization problems of large dimension and specific limitations cause the development of approximate methods, but these m

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9

Michalak, Krzysztof. "Low-Dimensional Euclidean Embedding for Visualization of Search Spaces in Combinatorial Optimization." IEEE Transactions on Evolutionary Computation 23, no. 2 (2019): 232–46. http://dx.doi.org/10.1109/tevc.2018.2846636.

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10

Nallaperuma, Samadhi, Frank Neumann, and Dirk Sudholt. "Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem." Evolutionary Computation 25, no. 4 (2017): 673–705. http://dx.doi.org/10.1162/evco_a_00199.

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Randomized search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to our theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed-time budget. We follow this approach and present a fixed-budget analysis for an NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson Problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve w

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Verdù, Federico Julian Camerota, Lorenzo Castelli, and Luca Bortolussi. "Scaling Combinatorial Optimization Neural Improvement Heuristics with Online Search and Adaptation." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 25 (2025): 27135–43. https://doi.org/10.1609/aaai.v39i25.34921.

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We introduce Limited Rollout Beam Search (LRBS), a beam search strategy for deep reinforcement learning (DRL) based combinatorial optimization improvement heuristics. Utilizing pre-trained models on the Euclidean Traveling Salesperson Problem, LRBS significantly enhances both in-distribution performance and generalization to larger problem instances, achieving optimality gaps that outperform existing improvement heuristics and narrowing the gap with state-of-the-art constructive methods. We also extend our analysis to two pickup and delivery TSP variants to validate our results. Finally, we em

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12

Linhares, Alexandre, and José R. A. Torreão. "Microcanonical Optimization Applied to the Traveling Salesman Problem." International Journal of Modern Physics C 09, no. 01 (1998): 133–46. http://dx.doi.org/10.1142/s012918319800011x.

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Optimization strategies based on simulated annealing and its variants have been extensively applied to the traveling salesman problem (TSP). Recently, there has appeared a new physics-based metaheuristic, called the microcanonical optimization algorithm (μO), which does not resort to annealing, and which has proven a superior alternative to the annealing procedures in various applications. Here we present the first performance evaluation of μO as applied to the TSP. When compared to three annealing strategies (simulated annealing, microcanonical annealing and Tsallis annealing), and to a tabu

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13

Steele, J. Michael. "Probabilistic and worst case analyses of classical problems of combinatorial optimization in Euclidean Space." Stochastic Processes and their Applications 26 (1987): 185. http://dx.doi.org/10.1016/0304-4149(87)90070-6.

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14

Steele, J. Michael. "Probabilistic and Worst Case Analyses of Classical Problems of Combinatorial Optimization in Euclidean Space." Mathematics of Operations Research 15, no. 4 (1990): 749–70. http://dx.doi.org/10.1287/moor.15.4.749.

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15

Koliechkina, L. M., and A. M. Nahirna. "Finding the Optimal Solution to the Problem of Conditional Optimization on the Graph of the set of Placements." Control Systems and Computers, no. 6 (290) (December 2020): 29–34. http://dx.doi.org/10.15407/csc.2020.06.029.

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The model of the problem of conditional optimization on the set of partial permutations is formulated. The linear form of the objective function is obtained by interpreting the elements of the set of partial permutations as points of the Euclidean space. A combinatorial polytope of allocations is considered for which there is a graph of the set of partial permutations An algorithm for solving this problem is proposed and its practical applicability is demonstrated. The proposed algorithm for solving the conditional optimization problem provides for the representation of the admissible of the S

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16

Jaillet, Patrick. "Rates of Convergence for Quasi-Additive Smooth Euclidean Functionals and Application to Combinatorial Optimization Problems." Mathematics of Operations Research 17, no. 4 (1992): 964–80. http://dx.doi.org/10.1287/moor.17.4.964.

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17

Yemets, O. A., and T. N. Barbolina. "Solution of Euclidean combinatorial optimization problems by the method of construction of a lexicographic equivalence." Cybernetics and Systems Analysis 40, no. 5 (2004): 726–34. http://dx.doi.org/10.1007/s10559-005-0010-2.

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18

Li, Gang, Hong Xi Wang, and Jian Zhuang. "Machinery Fault Detection Using Geodesic Distance Based on Genetic Clustering Algorithm." Advanced Materials Research 411 (November 2011): 572–75. http://dx.doi.org/10.4028/www.scientific.net/amr.411.572.

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Aim at the problem that there is an irregular data distribution when using multi-sensor to monitor machine conditions, a genetic clustering algorithm using geodesic distance metric (GCGD) is adopted to perform machine fault detection. In GCGD, a geodesic distance based proximity measure is employed replacing Euclidean distance that cannot correctly describe the relationship between data lying in a manifold, and GCGD determines partitioning of the feature vectors from a combinatorial optimization viewpoint. Fault detection experiments of inlet valve leakage in a two-stage reciprocating compress

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19

Kosolap, A. I. "Optimization In A Finite-Dimensional Euclide Space." Computer Modeling: Analysis, Control, Optimization 7, no. 1 (2020): 20–28. http://dx.doi.org/10.32434/2521-6406-2020-1-7-20-28.

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In this paper, optimization models in Euclidean space are divided into four complexity classes. Ef-fective algorithms have been developed to solve the problems of the first two classes of complexity. These are the primal-dual interior-point methods. Discrete and combinatorial optimization problems of the third complexity class are recommended to be converted to the fourth complexity class with continuous change of variables. Effective algorithms have not been developed for problems of the third and fourth complexity classes, with the exception of a narrow class of problems that are unimodal. T

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20

DU, HAI, WEILI WU, ZAIXIN LU, and YINFENG XU. "ON THE STEINER RATIO IN $\mathcal{R}_{n}$." Discrete Mathematics, Algorithms and Applications 03, no. 04 (2011): 473–89. http://dx.doi.org/10.1142/s1793830911001358.

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The Steiner minimum tree and the minimum spanning tree are two important problems in combinatorial optimization. Let P denote a finite set of points, called terminals, in the Euclidean space. A Steiner minimum tree of P, denoted by SMT(P), is a network with minimum length to interconnect all terminals, and a minimum spanning tree of P, denoted by MST(P), is also a minimum network interconnecting all the points in P, however, subject to the constraint that all the line segments in it have to terminate at terminals. Therefore, SMT(P) may contain points not in P, but MST(P) cannot contain such ki

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21

Yemets, Oleg A., and Natalya Yu Ustian. "Investigation of Solutions of Linear Problems of Euclidean Combinatorial Optimization on Permutations with Additional Restrictions. Part II." Journal of Automation and Information Sciences 43, no. 10 (2011): 56–63. http://dx.doi.org/10.1615/jautomatinfscien.v43.i10.60.

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22

Yemets, Oleg A., and Natalya Yu Ustian. "Investigation of Solutions of Linear Problems of Euclidean Combinatorial Optimization on Permutations with Additional Restrictions. Part I." Journal of Automation and Information Sciences 43, no. 3 (2011): 24–31. http://dx.doi.org/10.1615/jautomatinfscien.v43.i3.30.

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23

Yemets, Oleg A., and Natalya Yu Ustian. "Investigation of Solutions of Linear Problems of Euclidean Combinatorial Optimization on Permutations with Additional Restrictions. Part III." Journal of Automation and Information Sciences 44, no. 2 (2012): 30–37. http://dx.doi.org/10.1615/jautomatinfscien.v44.i2.30.

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24

Iemetsa, O. O., and O. O. Yemetsa. "Solving a linear problem of Euclidean combinatorial optimization on arrangements with the constant sum of the elements." Cybernetics and Systems Analysis 48, no. 4 (2012): 547–57. http://dx.doi.org/10.1007/s10559-012-9433-8.

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25

Qawqzeh, Yousef K., Ghaith Jaradat, Ali Al-Yousef, et al. "Applying the big bang-big crunch metaheuristic to large-sized operational problems." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 3 (2020): 2484. http://dx.doi.org/10.11591/ijece.v10i3.pp2484-2502.

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In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignme

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Yousef, K. Qawqzeh, Jaradat Ghaith, Al-Yousef Ali, et al. "Applying the big bang-big crunch metaheuristic to large-sized operational problems." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 3 (2020): 2484–502. https://doi.org/10.11591/ijece.v10i3.pp2484-2502.

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In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in as

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27

Barr, Joseph R., Peter Shaw, Faisal N. Abu-Khzam, Tyler Thatcher, and Sheng Yu. "Vulnerability Rating of Source Code with Token Embedding and Combinatorial Algorithms." International Journal of Semantic Computing 14, no. 04 (2020): 501–16. http://dx.doi.org/10.1142/s1793351x20500087.

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We present an empirical analysis of the source code of the Fluoride Bluetooth module, which is a part of standard Android OS distribution, by exhibiting a novel approach for classifying and scoring source code and vulnerability rating. Our workflow combines deep learning, combinatorial optimization, heuristics and machine learning. A combination of heuristics and deep learning is used to embed function (and method) labels into a low-dimensional Euclidean space. Because the corpus of the Fluoride source code is rather limited (containing approximately 12,000 functions), a straightforward embedd

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28

Zhu, Yi-Hang, Gilles Callebaut, Hatice Çalık, Liesbet Van der Perre, and François Rottenberg. "Energy Efficient Access Point Placement for Distributed Massive MIMO." Network 2, no. 2 (2022): 288–310. http://dx.doi.org/10.3390/network2020019.

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Distributed massive multiple-input multiple-output (D-mMIMO) is one of the key candidate technologies for future wireless networks. A D-mMIMO system has multiple, geographically distributed, access points (APs) jointly serving its users. First of all, this paper reports on where to position these APs to minimize the overall transmit power in actual deployments. As a second contribution, we show that it is essential to take into account both the radiation pattern of the antenna array and the environment information when optimizing AP placement. Neglecting the radiation pattern and environment i

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29

Pourhassan, Mojgan, and Frank Neumann. "Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem." Evolutionary Computation 27, no. 3 (2019): 525–58. http://dx.doi.org/10.1162/evco_a_00233.

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The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which metaheuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a cluster-based approach and a node-based approach, have been proposed by Hu and Raidl ( 2008 ) for solving this problem. In this article, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we poi

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30

Bykovsky, N. V., R. V. Harutyunyan, and A. V. Nasedkin. "Numerical modeling and optimization results for the placement of irregularly shaped elements on a multidimensional switching field with complex topology." T-Comm 18, no. 9 (2024): 48–54. https://doi.org/10.36724/2072-8735-2024-18-9-48-54.

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Numerical modeling was conducted to optimize the placement of irregularly shaped elements with non-standard dimensions on a multidimensional switching field with complex topology. The objective was to develop a method overcoming limitations of classical algorithms when dealing with complex geometric configurations. The methodological foundation was a combinatorial analog of the Gauss-Seidel method, adapted for discrete variables and multidimensional geometric constraints. Key features of the developed algorithm include integer encoding of element placement, accounting for non-standard componen

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31

Adasme, Pablo, Andrés Viveros, and Ali Dehghan Firoozabadi. "Quadratic p-Median Problem: A Bender’s Decomposition and a Meta-Heuristic Local-Based Approach." Symmetry 16, no. 9 (2024): 1114. http://dx.doi.org/10.3390/sym16091114.

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In this paper, the quadratic p-median optimization problem is discussed, where the goal is to connect users to a selected group of facilities (emergency services, telecommunications servers, healthcare facilities) at the lowest possible cost. The problem is aimed at minimizing the cost of connecting these selected facilities. The costs are symmetric, meaning connecting two different points is the same in both directions. This problem extends the traditional p-median problem, a combinatorial problem used in various fields like facility location, network design, transportation, supply chain netw

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32

Hou, Yue, Da Li, Di Zhang, and Zhiyuan Deng. "An Improved Phase Space Reconstruction Method-Based Hybrid Model for Chaotic Traffic Flow Prediction." Discrete Dynamics in Nature and Society 2022 (September 23, 2022): 1–22. http://dx.doi.org/10.1155/2022/5604674.

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Traffic flow is chaotic due to nonstationary realistic factors, and revealing the internal nonlinear dynamics of chaotic data and making high-accuracy predictions is the key to traffic control and inducement. Given that high-quality phase space reconstruction is the foundation of predictive modeling. Firstly, an improved C-C method based on the fused norm search domain is proposed to address the issue that the C-C method in the phase space reconstruction algorithm does not meet the Euclidean metric accuracy and reduces the reconstruction quality when the infinite norm metric is used. Secondly,

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33

Cvetkovic, Dragos. "Spectral recognition of graphs." Yugoslav Journal of Operations Research 22, no. 2 (2012): 145–61. http://dx.doi.org/10.2298/yjor120925025c.

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At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that

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34

Stoyan, Y. G., and S. V. Yakovlev. "Theory and Methods of Euclidian Combinatorial Optimization: Current Status and Prospects." Cybernetics and Systems Analysis 56, no. 3 (2020): 366–79. http://dx.doi.org/10.1007/s10559-020-00253-6.

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35

Yemets, Alexandra O. "Branch-and-Bound Method for Problems of the Euclidian Combinatorial Optimization on Combinations." Journal of Automation and Information Sciences 49, no. 5 (2017): 49–58. http://dx.doi.org/10.1615/jautomatinfscien.v49.i5.40.

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36

Luo, Songting, Leonidas J. Guibas, and Hong-Kai Zhao. "Euclidean skeletons using closest points." Inverse Problems & Imaging 5, no. 1 (2011): 95–113. http://dx.doi.org/10.3934/ipi.2011.5.95.

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37

Laksman, Efraim, Håkan Lennerstad, and Magnus Nilsson. "Improving bounds on the minimum Euclidean distance for block codes by inner distance measure optimization." Discrete Mathematics 310, no. 22 (2010): 3267–75. http://dx.doi.org/10.1016/j.disc.2010.04.025.

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38

Sourd, Francis. "Lexicographically minimizing axial motions for the Euclidean TSP." Journal of Combinatorial Optimization 19, no. 1 (2008): 1–15. http://dx.doi.org/10.1007/s10878-008-9154-0.

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39

Li, Jianping, Suding Liu, Junran Lichen, Wencheng Wang, and Yujie Zheng. "Approximation algorithms for solving the 1-line Euclidean minimum Steiner tree problem." Journal of Combinatorial Optimization 39, no. 2 (2019): 492–508. http://dx.doi.org/10.1007/s10878-019-00492-0.

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40

E Yarman, C., and B. Yazıcı. "A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group." Inverse Problems & Imaging 1, no. 3 (2007): 457–79. http://dx.doi.org/10.3934/ipi.2007.1.457.

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41

Goldman, Michael, and Dario Trevisan. "Optimal transport methods for combinatorial optimization over two random point sets." Probability Theory and Related Fields, November 7, 2023. http://dx.doi.org/10.1007/s00440-023-01245-1.

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AbstractWe investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $$\mathbb {R}^d$$ R d where the edge cost between two points is given by a pth power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows, of a suitable renormalization of the random minimum cost, if the points are uniformly distributed and $$d \ge 3, 1\le p<d$$ d ≥ 3 , 1 ≤ p < d . Previous results were limited to th

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42

Klootwijk, Stefan, and Bodo Manthey. "Probabilistic Analysis of Optimization Problems on Sparse Random Shortest Path Metrics." Algorithmica, August 26, 2023. http://dx.doi.org/10.1007/s00453-023-01167-3.

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AbstractSimple heuristics for (combinatorial) optimization problems often show a remarkable performance in practice. Worst-case analysis often falls short of explaining this performance. Because of this, “beyond worst-case analysis” of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many (combinatorial) optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a struct

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Lin, Fandel, and Hsun-Ping Hsieh. "A Grid-Based Two-Stage Parallel Matching Framework for Bi-Objective Euclidean Traveling Salesman Problem." ACM Transactions on Spatial Algorithms and Systems, April 7, 2022. http://dx.doi.org/10.1145/3526025.

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Traveling salesman problem (TSP) is one of the most studied combinatorial optimization problems; several exact, heuristic or even learning-based strategies have been proposed to solve this challenging issue. Targeting on the research problem of bi-objective non-monotonic Euclidean TSP and based on the concept of the multi-agent-based approach, we propose a two-stage parallel matching approaching for solving TSP. Acing as a divide-and-conquer strategy, the merit lies in the simultaneously clustering and routing in the dividing process. Precisely, we first propose the Two-Stage Parallel Matching

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Hirai, Hiroshi, and Motoki Ikeda. "A cost-scaling algorithm for computing the degree of determinants." computational complexity 31, no. 2 (2022). http://dx.doi.org/10.1007/s00037-022-00227-4.

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Abstract In this paper, we address computation of the degree $$\deg {\rm Det} A$$ deg Det A of Dieudonné determinant $${\rm Det} A$$ Det A of $$\begin{aligned} A = \sum_{k=1}^m A_k x_k t^{c_k}, \end{aligned}$$ A = ∑ k = 1 m A k x k t c k , where $$A_k$$ A k are $$n \times n$$ n × n matrices over a field $$\mathbb{K}$$ K , $$x_k$$ x k are noncommutative variables, t is a variable commuting with $$x_k$$ x k , $$c_k$$ c k are integers, and the degree is considered for t. This problem generalizes noncommutative Edmonds' problem and fundamental combinatorial optimization problems including the weig

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45

Y., Wang. "An Improved Method to Compute Sparse Graphs for Traveling Salesman Problem." International Journal of Mechanical, Industrial and Aerospace Sciences 11.0, no. 3 (2018). https://doi.org/10.5281/zenodo.1315719.

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The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is <em>O</em>(<em>CN</em><sub>max</sub><em>n</em><sup>2</sup>) where <em>C</em> is the iterations, <em>N</em><s

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46

Du Plessis, J. F., and Xerxes D. Arsiwalla. "A cosine rule-based discrete sectional curvature for graphs." Journal of Complex Networks 11, no. 4 (2023). http://dx.doi.org/10.1093/comnet/cnad022.

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Abstract How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analysing models of discrete spacetime in quantum gravity; inferring network geometry in network science; and manifold learning in data science. The key contribution of this article is to introduce and validate a new estimator of discrete sectional curvature for random graphs with low metric-distortion. The latter are constructed via a specific graph sprinkling method on different m

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47

Zhu, LiMin, HongGen Luo, and Han Ding. "Optimal Design of Measurement Point Layout for Workpiece Localization." Journal of Manufacturing Science and Engineering 131, no. 1 (2008). http://dx.doi.org/10.1115/1.3039515.

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This paper presents a methodology for the optimal design of the measurement point layout for 3D workpiece localization in the presence of part surface errors and measurement errors. A number of frame-invariant norms of the infinitesimal rigid body displacement, two of which give Riemann metrics on the Euclidean group, are defined to quantify the localization accuracy required by manufacturing processes. Then, two types of indices, both frame invariant and scale invariant, are derived to characterize the sensitivities of the accuracy measures to the sampling errors at the measurement points. Wi

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48

Gordeev, E. N., and O. G. Tarastsov. "The Steiner problem: a survey." Discrete Mathematics and Applications 3, no. 4 (1993). http://dx.doi.org/10.1515/dma-1993-0402.

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AbstractFor the past decade the Steiner minimal tree problem has attracted the attention of researchers in discrete optimization. A brief survey of the main results concerning the properties and algorithms of the Steiner problem in the Euclidean plane, the Steiner problem in the plane with rectilinear metric and the Steiner problem in networks is done in this paper. The main attention is paid to the recent results concerning the last problem.

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Krajewski, Adam M., Allison M. Beese, Wesley F. Reinhart, and Zi-Kui Liu. "Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning." npj Unconventional Computing 1, no. 1 (2024). http://dx.doi.org/10.1038/s44335-024-00012-2.

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AbstractDiverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discre

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50

Yan, Lili. "Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds." Inverse Problems and Imaging, 2022, 0. http://dx.doi.org/10.3934/ipi.2022034.

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<p style='text-indent:20px;'>We prove that a continuous potential <inline-formula><tex-math id="M1">\begin{document}$ q $\end{document}</tex-math></inline-formula> can be constructively determined from the knowledge of the Dirichlet–to–Neumann map for the perturbed biharmonic operator <inline-formula><tex-math id="M2">\begin{document}$ \Delta_g^2+q $\end{document}</tex-math></inline-formula> on a conformally transversally anisotropic Riemannian manifold of dimension <inline-formula><tex-math id="M3">\begin{document}$ \ge 3 $\end

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