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Journal articles on the topic 'Topologie en hypercube'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

ZIAVRAS, SOTIRIOS G., and MICHALIS A. SIDERAS. "FACILITATING HIGH-PERFORMANCE IMAGE ANALYSIS ON REDUCED HYPERCUBE (RH) PARALLEL COMPUTERS." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 04 (August 1995): 679–98. http://dx.doi.org/10.1142/s0218001495000262.

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The direct binary hypercube interconnection network has been very popular for the design of parallel computers, because it provides a low diameter and can emulate efficiently the majority of the topologies frequently employed in the development of algorithms. The last fifteen years have seen major efforts to develop image analysis algorithms for hypercube-based parallel computers. The results of these efforts have culminated in a large number of publications included in prestigious scholarly journals and conference proceedings. Nevertheless, the aforementioned powerful properties of the hypercube come at the cost of high VLSI complexity due to the increase in the number of communication ports and channels per PE (processing element) with an increase in the total number of PE’s. The high VLSI complexity of hypercube systems is undoubtedly their dominant drawback; it results in the construction of systems that contain either a large number of primitive PE’s or a small number of powerful PE’s. Therefore, low-dimensional k-ary n-cubes with lower VSLI complexity have recently drawn the attention of many designers of parallel computers. Alternative solutions reduce the hypercube’s VLSI complexity without jeopardizing its performance. Such an effort by Ziavras has resulted in the introduction of reduced hypercubes (RH’s). Taking advantage of existing high-performance routing techniques, such as wormhole routing, an RH is obtained by a uniform reduction in the number of edges for each hypercube node. An RH can also be viewed as several connected copies of the well-known cube-connected-cycles network. The objective here is to prove that parallel computers comprising RH interconnection networks are definitely good choices for all levels of image analysis. Since the exact requirements of high-level image analysis are difficult to identify, but it is believed that versatile interconnection networks, such as the hypercube, are suitable for relevant tasks, we investigate the problem of emulating hypercubes on RH’s. The ring (or linear array), the torus (or mesh), and the binary tree are the most frequently used topologies for the development of algorithms in low-level and intermediate-level image analysis. Thus, to prove the viability of the RH for the two lower levels of image analysis, we introduce techniques for embedding the aforementioned three topologies into RH’s. The results prove the suitability of RH’s for all levels of image analysis.

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Das, Sajal K., Sabine Öhring, and Amit K. Banerjee. "Embeddings into Hyper Petersen Networks: Yet Another Hypercube-Like Interconnection Topology." VLSI Design 2, no. 4 (January 1, 1995): 335–51. http://dx.doi.org/10.1155/1995/95759.

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A new hypercube-like topology, called the hyper Petersen (HP) network, is proposed and analyzed, which is constructed from the well-known cartesian product of the binary hypercube and the Petersen graph of ten nodes.This topology is an attractive candidate for multiprocessor interconnection having such desirable properties as regularity, high symmetry and connectivity, and logarithmic diameter. For example, an n-dimensional hyper Petersen network, HPn, with N=1.25 * 2n nodes is a regular graph of degree and node-connectivity n and diameter n–1 , whereas an (n–1)-dimensional binary hypercube, Qn−1 , with the same diameter covers only 2n−1 nodes, each of degree (n–1). Thus the HP topology accommodates 2.5 times extra nodes than Qn−1 at the cost of increasing the node-degree by one. With the same degree and connectivity of n, the diameter of the HPn network is one less than that of Qn, yet having 1.25 times larger number of nodes.Efficient routing and broadcasting schemes are presented, and node-disjoint paths in HPn, are computed even under faulty conditions. The versatility of the hyper Petersen networks is emphasized by embedding rings, meshes, hypercubes and several tree-related topologies into it. Contrary to the hypercubes, rings of odd lengths, and a complete binary tree of height n–1 permit subgraph embeddings in HPn.

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3

BOSSARD, ANTOINE. "ON THE DECYCLING PROBLEM IN HIERARCHICAL HYPERCUBES." Journal of Interconnection Networks 14, no. 02 (June 2013): 1350006. http://dx.doi.org/10.1142/s0219265913500060.

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Due to the huge number of CPU nodes involved in modern supercomputers, efficient CPU connection is challenging, and legacy simple network topologies such as hypercubes are no more suitable for physical reasons. The hierarchical hypercube (HHC) has been designed as a topology for interconnection network of massively parallel systems. An HHC is effectively able to link many nodes while retaining a low degree and a small diameter compared to a hypercube of the same size. In this paper, we address a fundamental problem inside an HHC, the decycling problem, which consists of finding a set of nodes as small as possible such that excluding these nodes from the network ensures a cycle-free topology. This problem has many important applications such as lock-free resource allocation and concurrent access. So, we propose in this paper an efficient algorithm finding in an HHC a decycling set of competitively small size.

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4

PANAGIOTOU, KONSTANTINOS, XAVIER PÉREZ-GIMÉNEZ, THOMAS SAUERWALD, and HE SUN. "Randomized Rumour Spreading: The Effect of the Network Topology." Combinatorics, Probability and Computing 24, no. 2 (May 6, 2014): 457–79. http://dx.doi.org/10.1017/s0963548314000194.

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We consider the popular and well-studied push model, which is used to spread information in a given network with n vertices. Initially, some vertex owns a rumour and passes it to one of its neighbours, which is chosen randomly. In each of the succeeding rounds, every vertex that knows the rumour informs a random neighbour. It has been shown on various network topologies that this algorithm succeeds in spreading the rumour within O(log n) rounds. However, many studies are quite coarse and involve huge constants that do not allow for a direct comparison between different network topologies. In this paper, we analyse the push model on several important families of graphs, and obtain tight runtime estimates. We first show that, for any almost-regular graph on n vertices with small spectral expansion, rumour spreading completes after log2n + log n+o(log n) rounds with high probability. This is the first result that exhibits a general graph class for which rumour spreading is essentially as fast as on complete graphs. Moreover, for the random graph G(n,p) with p=c log n/n, where c > 1, we determine the runtime of rumour spreading to be log2n + γ (c)log n with high probability, where γ(c) = clog(c/(c−1)). In particular, this shows that the assumption of almost regularity in our first result is necessary. Finally, for a hypercube on n=2d vertices, the runtime is with high probability at least (1+β) ⋅ (log2n + log n), where β > 0. This reveals that the push model on hypercubes is slower than on complete graphs, and thus shows that the assumption of small spectral expansion in our first result is also necessary. In addition, our results combined with the upper bound of O(log n) for the hypercube (see [11]) imply that the push model is faster on hypercubes than on a random graph G(n, clog n/n), where c is sufficiently close to 1.

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5

REHIDA, P., and I. KOMISAROV. "COMPARISON OF PLANNING RESULTS USING BUBBLE SCHEDULING AND ALLOCATION (BSA) ALGORITHM FOR DIFFERENT TOPOLOGIES." HERALD OF KHMELNYTSKYI NATIONAL UNIVERSITY 295, no. 2 (May 2021): 89–96. http://dx.doi.org/10.31891/2307-5732-2021-295-2-89-96.

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In this article, the bubble scheduling and allocation algorithm is considered for different types of topologies: grid, hypercube, de Bruijn topology, extended de Bruijn topology based on ternary code. Static planning algorithms are analyzed; the results are presented in the form of a comparative table on the criteria of complexity, the need to find a critical path, the presence of a table of routing and efficiency. The study of the method of planning calculations is carried out based on the problem of finding the roots of systems of linear and nonlinear equations using Cramer’s and Newton’s methods. The corresponding graphs of tier-parallel form are synthesized for these methods. The principles of synthesis for 4 types of topologies are shown. The synthesis of the grid, hypercube, and de Bruijn graph is considered in the classical form. The synthesis of the extended de Bruijn topology is a synthesis of de Bruijn topology [1, 2] using a ternary code. That is, with the same number of processors, the number of connections increases. Experimental studies of the scheduling of the obtained graphs in the synthesized topologies using the method of bubble scheduling and allocation are conducted; the results of scheduling are presented for these topologies. The best results were shown by extended de Bruijn topology based on ternary code due to the increased degree of units, which is especially noticeable for Newton’s method where there are much more data transfers than in Cramer’s method. The topology of a hypercube and de Bruijn topology demonstrated just about same results but hypercube topology did a little better. In addition to this, having a smaller diameter and cost, the hypercube is the most optimal topology and still used today. However, when constructing fail-safe topological organizations, it is better to use topologies based on ternary code, such as the topology based on the extended de Bruijn graph.

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Sabino, Alan U., Miguel F. S. Vasconcelos, Yuefan Deng, and Alexandre F. Ramos. "Symmetry-guided design of topologies for supercomputer networks." International Journal of Modern Physics C 29, no. 07 (July 2018): 1850048. http://dx.doi.org/10.1142/s0129183118500481.

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A family of graphs optimized as the topologies for interconnection networks is proposed. The needs of such topologies with minimal diameters and minimal mean path lengths are met by special constructions of the weight vectors in a representation of the symplectic algebra. Such design of topologies can conveniently reconstruct the mesh and hypercube, widely used as network topologies, as well as many other classes of graphs potentially suitable for network topologies.

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7

Alahmadi, Adel, Husain Alhazmi, Shakir Ali, Michel Deza, Mathieu Dutour Sikirić, and Patrick Solé. "Hypercube emulation of interconnection networks topologies." Mathematical Methods in the Applied Sciences 39, no. 16 (January 4, 2016): 4856–65. http://dx.doi.org/10.1002/mma.3820.

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8

Heun, V. "Efficient Embeddings into Hypercube-like Topologies." Computer Journal 46, no. 6 (June 1, 2003): 632–44. http://dx.doi.org/10.1093/comjnl/46.6.632.

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9

Tzeng, Nian-Feng. "Analysis of a variant hypercube topology." ACM SIGARCH Computer Architecture News 18, no. 3b (September 1990): 60–70. http://dx.doi.org/10.1145/255129.255140.

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10

Loutskii, Heorhii, Artem Volokyta, Pavlo Rehida, and Olexandr Goncharenko. "USING EXCESS CODE TO DESIGN FAULT-TOLERANT TOPOLOGIES." TECHNICAL SCIENCES AND TECHNOLOGIES, no. 1 (15) (2019): 134–44. http://dx.doi.org/10.25140/2411-5363-2019-1(15)-134-144.

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and in modernizing an already existing one. Particular attention is paid to it when building multicomputer systems or clusters. The most interesting ways to increase fault tolerance is to use the topological structure of the system to bypass the malfunction and use one or another element of the system to replace the faulty. Of course, this requires the development of a specific topology. The article deals with the development of fault-tolerant versions of popular topologies, such as quasiquantum and hypercube, based on the excess code 0/1 /-1. Target setting. An important part of any multicomputer system or cluster is its topological structure. This structure defines the routing of messages in the system, speed of message transmission, and level of fault-tolerance of a system. The article proposes a method for increasing fault-tolerance based on the use of excess code. Actual scientific researches and issues analysis. Synthesis of topologies such as the hypercube or the de Bruin topology is well studied and described now, there are papers consider methods for increasing the fault-tolerance that based on usage of additional nodes that duplicate current nodes. Other papers consider using a tree-based routing to improve fault-tolerance of the system. Uninvestigated parts of general matters defining. Now the possibilities of using excess code 0/1/-1 for creating new fault-tolerant topologies based on existing synthesis methods are unconsidered. The research objective. The task is to describe the synthesis of fault tolerant topologies, the consideration of the possibilities of using their features and the analysis of the main characteristics in comparison with each other and with classic versions based on binary code. The statement of basic materials. The synthesis of hypercube and de Bruin topology is described on the basis of the usual binary code and the redundant code 0/1 / -1, the possibilities of using redundancy are considered, first of all, to increase the fault-tolerance, a comparative analysis of all of these topologies is carried out. Conclusions. The analysis of characteristics is performed, the main advantages and disadvantages of the proposed topological structures are highlighted, suggestions for their improvement are made.

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11

Gonzalez, A., M. Valero-Garcia, and L. Diaz de Cerio. "Executing algorithms with hypercube topology on torus multicomputers." IEEE Transactions on Parallel and Distributed Systems 6, no. 8 (1995): 803–14. http://dx.doi.org/10.1109/71.406957.

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12

Erd�s, P�l, Peter Hamburger, Raymond E. Pippert, and William D. Weakley. "Hypercube subgraphs with minimal detours." Journal of Graph Theory 23, no. 2 (October 1996): 119–28. http://dx.doi.org/10.1002/(sici)1097-0118(199610)23:2<119::aid-jgt3>3.0.co;2-w.

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13

Dvo?�k, Tom�?k, Ivan Havel, Jean-Marie Laborde, and Michel Mollard. "Spanning caterpillars of a hypercube." Journal of Graph Theory 24, no. 1 (January 1997): 9–19. http://dx.doi.org/10.1002/(sici)1097-0118(199701)24:1<9::aid-jgt2>3.0.co;2-v.

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14

Hamburger, Peter, Alexandr V. Kostochka, and Alexander Sidorenko. "Hypercube subgraphs with local detours." Journal of Graph Theory 30, no. 2 (February 1999): 101–11. http://dx.doi.org/10.1002/(sici)1097-0118(199902)30:2<101::aid-jgt4>3.0.co;2-9.

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15

BERTHOLD, JOST, and RITA LOOGEN. "THE IMPACT OF DYNAMIC CHANNELS ON FUNCTIONAL TOPOLOGY SKELETONS." Parallel Processing Letters 18, no. 01 (March 2008): 101–15. http://dx.doi.org/10.1142/s0129626408003259.

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Parallel functional programs with implicit communication often generate purely hierarchical communication topologies during execution: communication only happens between parent and child processes. Hence, messages between siblings must be passed via the parent causing inefficiencies that can be avoided by direct communication between arbitrary processes. The Eden parallel functional language provides dynamic channels to implement arbitrary communication topologies. This paper analyses the impact of dynamic channels on Eden's topology skeletons, i.e. skeletons which define process topologies such as rings, toroids, or hypercubes. We compare topology skeletons with and without dynamic channels with respect to runtime and communication. Our case studies confirm that dynamic channels decrease the number of messages by up to 50% and substantially reduce runtime. Detailed analyses of EdenTV (Eden trace viewer) execution profiles reveal a bottleneck in the root process when only hierarchical channel connections are used and a better distribution of communications with dynamic channels.

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16

Alon, Noga, Radoš Radoičić, Benny Sudakov, and Jan Vondrák. "A Ramsey-type result for the hypercube." Journal of Graph Theory 53, no. 3 (2006): 196–208. http://dx.doi.org/10.1002/jgt.20181.

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17

Ghozati, S. A., and T. Smires. "The fastcube: a variation on hypercube topology with lower diameter." Computers & Electrical Engineering 29, no. 1 (January 2003): 151–71. http://dx.doi.org/10.1016/s0045-7906(01)00021-0.

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18

Qi, Heng, Yang Li, Keqiu Li, and Milos Stojmenovic. "An exchanged folded hypercube-based topology structure for interconnection networks." Concurrency and Computation: Practice and Experience 27, no. 16 (May 18, 2015): 4194–210. http://dx.doi.org/10.1002/cpe.3506.

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19

YE, TAI-LING, DUN-WEI CHENG, and SUN-YUAN HSIEH. "Improved Precise Fault Diagnosis Algorithm for Hypercube-Like Systems Based on the Comparison Diagnosis Model." Journal of Interconnection Networks 16, no. 03n04 (September 2016): 1650009. http://dx.doi.org/10.1142/s0219265916500092.

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Multiprocessor systems are being increasingly adopted and the system reliability is an important perspective for multiprocessor systems. The fault diagnosis has become crucial for achieving high reliability in multiprocessor systems. The precise fault diagnosis diagnoses all processors correctly. In the comparison-based model, it allows a processor to perform diagnosis by contrasting the responses from a pair of neighboring processors through sending the identical assignment. On the basis of comparison-based model, Sengupta and Dahbura (“On self-diagnosable multiprocessor systems: diagnosis by the comparison approach,” IEEE Transaction on Computers, vol. 41, no. 11, pp. 1386–1396, 1992) put forward the MM* model, any processor c diagnoses two processors c1 and c2 if c has direct communication links to them. Sengupta and Dahbura also designed an O(N5)-time precise fault diagnosis algorithm to diagnose faulty processors for general topologies by using the MM* model, where N is the cardinality of processor set in multiprocessor systems. Lately, Ye and Hsieh (“A scalable comparison-based diagnosis algorithm for hypercube-like net-works,” IEEE Transaction on Reliability, vol. 62, no. 4, pp. 789–799, 2013) devised an precise fault diagnosis algorithm to diagnose all faulty processors for hypercube-like networks by using the MM* model with O(N(log2N)2) time complexity. On the basis of Hamiltonian cycle properties, we improve the aforementioned results by presenting an O(N)-time precise fault diagnosis algorithm to diagnose all faulty processors for hypercube-like networks by using the MM* model.

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20

Arizumi, Nana, Peter Hamburger, and Alexandr Kostochka. "Onk-detour subgraphs of hypercubes." Journal of Graph Theory 57, no. 1 (2007): 55–64. http://dx.doi.org/10.1002/jgt.20281.

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21

Casselgren, Carl Johan, Klas Markström, and Lan Anh Pham. "Edge precoloring extension of hypercubes." Journal of Graph Theory 95, no. 3 (March 20, 2020): 410–44. http://dx.doi.org/10.1002/jgt.22561.

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22

Havel, I., and P. Liebl. "One-legged caterpillars span hypercubes." Journal of Graph Theory 10, no. 1 (1986): 69–77. http://dx.doi.org/10.1002/jgt.3190100110.

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23

Conder, Marston. "Hexagon-free subgraphs of hypercubes." Journal of Graph Theory 17, no. 4 (September 1993): 477–79. http://dx.doi.org/10.1002/jgt.3190170405.

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24

Wilker, J. B. "An extremum problem for hypercubes." Journal of Geometry 55, no. 1-2 (March 1996): 174–81. http://dx.doi.org/10.1007/bf01223043.

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25

Stanley, Kenneth O., David B. D'Ambrosio, and Jason Gauci. "A Hypercube-Based Encoding for Evolving Large-Scale Neural Networks." Artificial Life 15, no. 2 (April 2009): 185–212. http://dx.doi.org/10.1162/artl.2009.15.2.15202.

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Research in neuroevolution—that is, evolving artificial neural networks (ANNs) through evolutionary algorithms—is inspired by the evolution of biological brains, which can contain trillions of connections. Yet while neuroevolution has produced successful results, the scale of natural brains remains far beyond reach. This article presents a method called hypercube-based NeuroEvolution of Augmenting Topologies (HyperNEAT) that aims to narrow this gap. HyperNEAT employs an indirect encoding called connective compositional pattern-producing networks (CPPNs) that can produce connectivity patterns with symmetries and repeating motifs by interpreting spatial patterns generated within a hypercube as connectivity patterns in a lower-dimensional space. This approach can exploit the geometry of the task by mapping its regularities onto the topology of the network, thereby shifting problem difficulty away from dimensionality to the underlying problem structure. Furthermore, connective CPPNs can represent the same connectivity pattern at any resolution, allowing ANNs to scale to new numbers of inputs and outputs without further evolution. HyperNEAT is demonstrated through visual discrimination and food-gathering tasks, including successful visual discrimination networks containing over eight million connections. The main conclusion is that the ability to explore the space of regular connectivity patterns opens up a new class of complex high-dimensional tasks to neuroevolution.

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AL-AYYOUB, ABDEL-ELAH, and KHALED DAY. "FAST LU FACTORIZATION ON THE HYPERSTAR INTERCONNECTION NETWORK." Journal of Interconnection Networks 03, no. 03n04 (September 2002): 231–43. http://dx.doi.org/10.1142/s0219265902000641.

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The hyperstar network has been recently proposed as an attractive product network that outperforms many popular topologies in various respects. In this paper we explore additional capabilities for the hyperstar network through an efficient parallel algorithm for solving the LU factorization problem on this network. The proposed parallel algorithm uses O(n) communication time on a hyperstar formed by the cross-product of two n-star graphs. This communication time improves the best known result for the hypercube-based LU factorization by a factor of log(n), and improves the best known result for the mesh-based LU factorization by a factor of (n - 1)!.

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Marie Deza, Michel, Mathieu Dutour Sikirić, and Sergey Shpectorov. "Hypercube embedding of Wythoffians." Ars Mathematica Contemporanea 1, no. 1 (August 22, 2008): 99–111. http://dx.doi.org/10.26493/1855-3974.26.6c7.

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28

GARCIA, ROMAN, and JOSE DUATO. "SUBOPTIMAL-OPTIMAL ROUTING FOR LAN INTERNETWORKING USING TRANSPARENT BRIDGES." International Journal of Foundations of Computer Science 09, no. 02 (June 1998): 139–56. http://dx.doi.org/10.1142/s0129054198000118.

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The current standard transparent bridge protocol IEEE-802.1D is based on the Spanning Tree (ST) algorithm. It has a very important restriction: it cannot work when the topology has active loops. Therefore, a tree is the only possible interconnection topology that can be used. The ST algorithm guarantees that the active topology is a tree discarding lines that form loops. However, because of this, network bandwidth cannot be fully utilized. Moreover, trees have a very serious bottleneck near the root. This paper proposes a new transparent bridge protocol for LAN interconnection that allows active loops. Therefore, strongly connected regular topologies like tori, hypercubes, meshes, etc., as well as irregular topologies can be used without wasting bandwidth. As loops provide alternative paths, the new protocol (named OSR for Optimal-Suboptimal Routing) uses optimal routing or, in the worst case, suboptimal routing.

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Almobaidee, Wesam, Mohammad Qatawneh ., Azzam Sleit ., Imad Salah ., and Saleh Al-Sharaeh . "Efficient Mapping Scheme of Ring Topology Onto Tree-Hypercubes." Journal of Applied Sciences 7, no. 18 (September 1, 2007): 2666–70. http://dx.doi.org/10.3923/jas.2007.2666.2670.

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30

Malluhi, Q. M., and M. A. Bayoumi. "The hierarchical hypercube: a new interconnection topology for massively parallel systems." IEEE Transactions on Parallel and Distributed Systems 5, no. 1 (1994): 17–30. http://dx.doi.org/10.1109/71.262585.

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Chung, Fan R. K. "Subgraphs of a hypercube containing no small even cycles." Journal of Graph Theory 16, no. 3 (July 1992): 273–86. http://dx.doi.org/10.1002/jgt.3190160311.

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Lässig, Jörg, and Dirk Sudholt. "General Upper Bounds on the Runtime of Parallel Evolutionary Algorithms*." Evolutionary Computation 22, no. 3 (September 2014): 405–37. http://dx.doi.org/10.1162/evco_a_00114.

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We present a general method for analyzing the runtime of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel runtime. This allows for a rigorous estimate of the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the performance guarantees improve with the density of the topology. Surprisingly, even sparse topologies such as ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors lead to the best guaranteed speedups, thus giving hints on how to parameterize parallel evolutionary algorithms.

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33

Liu, Yu-Liang, and Jou-Ming Chang. "Realizing Exchanged Crossed Cube Communication Patterns on Linear Array WDM Optical Networks." International Journal of Foundations of Computer Science 29, no. 06 (September 2018): 1003–21. http://dx.doi.org/10.1142/s0129054118500181.

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The exchanged crossed cube, denoted by [Formula: see text], is a novel interconnection network with fewer edges and smaller diameter compared to other variations of the corresponding hypercube. The linear array, denoted by [Formula: see text], is one of the most popular topologies in optical networks. This paper addresses the routing and wavelength assignment for realizing [Formula: see text] communication pattern on wavelength division multiplexing (WDM) optical network [Formula: see text], where [Formula: see text]. We prove that the congestion for [Formula: see text] on [Formula: see text] is equal to [Formula: see text], which is the lower bound of the minimum number of required wavelengths. In addition, an embedding scheme and an optimal wavelength assignment algorithm that achieve this bound are also proposed.

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Blial, Othmane, Mouad Ben Mamoun, and Redouane Benaini. "OMCH-SDN: An Overlay multi-controller Hypercube-based topology for Softwaredefined Networks." International Journal of Engineering and Technology 10, no. 2 (April 30, 2018): 476–83. http://dx.doi.org/10.21817/ijet/2018/v10i2/181002030.

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A. Hnaif, Adnan, Abdelfatah A. Tamimi, Ayman M. Abdalla, and Iqbal Jebril. "A Fault-Handling Method for the Hamiltonian Cycle in the Hypercube Topology." Computers, Materials & Continua 68, no. 1 (2021): 505–19. http://dx.doi.org/10.32604/cmc.2021.016123.

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Das, Shouman. "Genus of the hypercube graph and real moment-angle complexes." Topology and its Applications 258 (May 2019): 415–24. http://dx.doi.org/10.1016/j.topol.2019.03.009.

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37

Kalamuddin, Mohd, and Mohd Husain. "A Comparatively Analysis and Performance of Logical Topologies of Embedded Hypercube (LTOEH) Interconnection Network." International Journal of Computer Applications 132, no. 9 (December 17, 2015): 22–30. http://dx.doi.org/10.5120/ijca2015907535.

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Qiu, Ke, and Sajal K. Das. "Interconnection Networks and Their Eigenvalues." International Journal of Foundations of Computer Science 14, no. 03 (June 2003): 371–89. http://dx.doi.org/10.1142/s0129054103001790.

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Interconnection networks of various topologies have been widely used in designing multiprocessor architectures. Study of graph theoretical or combinatorial properties of such networks help us better understand them, as well as develop on these architectures more efficient parallel algorithms including fault-tolerant communication/routing algorithms. In this paper, we analyze a broad class of interconnection networks from a new angle by looking into the corresponding graph spectra (i.e., eigenvalues and their multiplicities). Since eigenvalues of the edjacency matrix of a graph can reveal many important properties of the graph that are closely related to its combinatorial invariants, we believe that the study of spectra of interconnection networks can be a more unified approach to studying their topological properties. As a first step) in this direction, here we mainly concentrate on finding out the spectra of some of the most studied interconnection networks. Specifically, after a brief survey of results that relate spectra of graphs to their structural properties, we summarize the existing results for eigenvalues and multiplicities of several popular interconnection networks such as the hypercube and mesh. We also derive some of these results in a more straightforward way. Then we present new results on spectra for some other known networks such as the line graph of the hypercube, followed by experimental results on a few others including the star and pancake networks.

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DUATO, JOSÉ. "ON THE DESIGN OF DEADLOCK-FREE ADAPTIVE MULTICAST ROUTING ALGORITHMS." Parallel Processing Letters 03, no. 04 (December 1993): 321–33. http://dx.doi.org/10.1142/s0129626493000368.

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Multicast communication refers to the delivery of the same message from one source node to an arbitrary number of destination nodes. Two multicast wormhole routing methods have been presented in [13] for multicomputers with 2D-mesh and hypercube topologies. Also, a theory for the design of deadlock-free adaptive routing algorithms for wormhole networks has been proposed in [7, 8]. This theory supplies the sufficient conditions for an adaptive routing algorithm to be deadlock-free, even when there are cyclic dependencies between channels. This paper analyses the additional channel dependencies produced by multicast routing algorithms on wormhole networks. Then, the theory proposed in [7, 8] is extended by considering them. As an example, the multicast routing algorithms presented in [13] are extended, taking advantage of the alternative paths offered by the network.

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da Silva, Ilda P. F. "Recursivity and geometry of the hypercube." Linear Algebra and its Applications 397 (March 2005): 223–33. http://dx.doi.org/10.1016/j.laa.2004.10.016.

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Faria, Luerbio, Celina Miraglia Herrera de Figueiredo, Ondrej Sýkora, and Imrich Vrt'o. "An improved upper bound on the crossing number of the hypercube." Journal of Graph Theory 59, no. 2 (October 2008): 145–61. http://dx.doi.org/10.1002/jgt.20330.

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Zhou, Jin-Xin, Jin Ho Kwak, Yan-Quan Feng, and Zhen-Lin Wu. "Automorphism group of the balanced hypercube." Ars Mathematica Contemporanea 12, no. 1 (November 12, 2016): 145–54. http://dx.doi.org/10.26493/1855-3974.825.a76.

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Banerjee, S., and D. Sarkar. "Hypercube connected rings: a scalable and fault-tolerant logical topology for optical networks." Computer Communications 24, no. 11 (June 2001): 1060–79. http://dx.doi.org/10.1016/s0140-3664(00)00336-4.

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LI, CHENKUAN, THOMAS E. HART, KEVIN J. HENRY, and IAN A. NEUFELD. "AVERAGE-CASE "MESSY" BROADCASTING." Journal of Interconnection Networks 09, no. 04 (December 2008): 487–505. http://dx.doi.org/10.1142/s0219265908002400.

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Current studies of "messy" broadcasting have so far concentrated on finding worst-case times. However, such worst-case scenarios are extremely unlikely to occur in general. Hence, determining average-case times or tight upper bounds for completing "messy" broadcasting in various network topologies is both necessary and meaningful in practice. In this paper, we focus on seeking the average-case "messy" broadcast times of stars, paths, cycles, and d-ary trees, and finding good upper bounds for hypercubes. Finally, we derive a recursive formula to express the average-case time for a specific "messy" broadcast model on a complete graph using a classical occupancy problem in probability theory, and provide a nice simulation result which indicates that this model behaves like classical broadcasting.

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Melent'ev, Victor Aleksandrovich. "FAULT-TOLERANCE OF HYPERCUBIC AND COMPACT TOPOLOGY OF COMPUTING SYSTEMS." Theoretical & Applied Science 44, no. 12 (December 30, 2016): 98–105. http://dx.doi.org/10.15863/tas.2016.12.44.20.

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Barini, Geoffrey O., Livingstone M. Ngoo, and Ronald W. Mwangi. "Application of a fuzzy unit hypercube in cardiovascular risk classification." Soft Computing 23, no. 23 (January 30, 2019): 12521–27. http://dx.doi.org/10.1007/s00500-019-03802-0.

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Maciel, Oscar, Arturo Valdivia, Diego Oliva, Erik Cuevas, Daniel Zaldívar, and Marco Pérez-Cisneros. "A novel hybrid metaheuristic optimization method: hypercube natural aggregation algorithm." Soft Computing 24, no. 12 (October 23, 2019): 8823–56. http://dx.doi.org/10.1007/s00500-019-04416-2.

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Risi, Sebastian, and Kenneth O. Stanley. "An Enhanced Hypercube-Based Encoding for Evolving the Placement, Density, and Connectivity of Neurons." Artificial Life 18, no. 4 (October 2012): 331–63. http://dx.doi.org/10.1162/artl_a_00071.

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Intelligence in nature is the product of living brains, which are themselves the product of natural evolution. Although researchers in the field of neuroevolution (NE) attempt to recapitulate this process, artificial neural networks (ANNs) so far evolved through NE algorithms do not match the distinctive capabilities of biological brains. The recently introduced hypercube-based neuroevolution of augmenting topologies (HyperNEAT) approach narrowed this gap by demonstrating that the pattern of weights across the connectivity of an ANN can be generated as a function of its geometry, thereby allowing large ANNs to be evolved for high-dimensional problems. Yet the positions and number of the neurons connected through this approach must be decided a priori by the user and, unlike in living brains, cannot change during evolution. Evolvable-substrate HyperNEAT (ES-HyperNEAT), introduced in this article, addresses this limitation by automatically deducing the node geometry from implicit information in the pattern of weights encoded by HyperNEAT, thereby avoiding the need to evolve explicit placement. This approach not only can evolve the location of every neuron in the network, but also can represent regions of varying density, which means resolution can increase holistically over evolution. ES-HyperNEAT is demonstrated through multi-task, maze navigation, and modular retina domains, revealing that the ANNs generated by this new approach assume natural properties such as neural topography and geometric regularity. Also importantly, ES-HyperNEAT's compact indirect encoding can be seeded to begin with a bias toward a desired class of ANN topographies, which facilitates the evolutionary search. The main conclusion is that ES-HyperNEAT significantly expands the scope of neural structures that evolution can discover.

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de Berg, Mark, Haggai David, Matthew J. Katz, Mark Overmars, A. Frank van der Stappen, and Jules Vleugels. "Guarding scenes against invasive hypercubes." Computational Geometry 26, no. 2 (October 2003): 99–117. http://dx.doi.org/10.1016/s0925-7721(03)00016-6.

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JenChih Lin. "A Balanced Load Algorithm for Embedding Some Network Topologies in an Incrementally Extensible Hypercube with Unbounded Expansion." INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences 5, no. 7 (April 15, 2013): 282–90. http://dx.doi.org/10.4156/aiss.vol5.issue7.34.

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