research-article

Embedding Cube-Connected Cycles into Grid Network for Minimum Wirelength

Authors:

Xiaoyu DuAuthors Info & Claims

WI-IAT '21: IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology

Pages 461 - 465

https://doi.org/10.1145/3498851.3498998

Published: 11 April 2022 Publication History

Abstract

There is a trade-off problem among diameter, scalability and path length of structure designing in Data Center Network. Therefore, many papers had provided the solution called embeddability, which is an indicator to measure the ability of combining advantages of different networks. This paper considered grid embeddings as an example because they have many applications such as simulation capabilities of a parallel architecture, designing VLSI layout etc. As a modification of the hypercube, Cube-Connected Cycles (CCC) has good symmetry, low diameter and strong connectivity. In this paper, we focused on the minimum wirelength in the linear layout and grid layout of the CCC. Firstly, we analyzed the recursive structure characteristics and properties of CCC. Then, the maximum induced subgraph of CCC is obtained by theoretical analysis. Next, an embedded mode is proposed to layout CCC onto a linear array and we derived an exact formula for the minimum wirelength. Furthermore, we devised an optimal embedding of the n-dimensional CCC onto a grid network.

References

[1]

A Ajs, B Ja, and B Ma. 2020. A linear time algorithm for embedding locally twisted cube into grid network to optimize the layout. Discrete Applied Mathematics 286 (2020), 10–18.

[2]

Micheal Arockiaraj, Jessie Abraham, Jasintha Quadras, and Arul Jeya Shalini. 2017. Linear layout of locally twisted cubes. International Journal of Computer Mathematics 94, 1(2017), 56–65.

Digital Library

[3]

S. L. Bezrukov, J. D. Chavez, L. H. Harper, M. Rottger, and U. P. Schroeder. 1999. Embedding of Hypercubes into Grids. Lecture Notes in Computer Science(1999).

[4]

Alfred J Boals, Ajay K Gupta, and Naveed A Sherwani. 1994. Incomplete hypercubes: Algorithms and embeddings. The Journal of Supercomputing 8, 3 (1994), 263–294.

Digital Library

[5]

Jehoshua Bruck, Robert Cypher, and Danny Soroker. 1994. Embedding cube-connected cycles graphs into faulty hypercubes. IEEE Trans. Comput. 43, 10 (1994), 1210–1220.

Digital Library

[6]

Guihai Chen and Francis CM Lau. 2000. Tighter layouts of the cube-connected cycles. IEEE Transactions on Parallel and Distributed Systems 11, 2 (2000), 182–191.

Digital Library

[7]

Kemal Efe. 1991. A variation on the hypercube with lower diameter. IEEE Transactions on computers 40, 11 (1991), 1312–1316.

Digital Library

[8]

W. Fan, J. Fan, Z. Han, P. Li, Y. Zhang, and R. Wang. 2021. Fault-tolerant hamiltonian cycles and paths embedding into locally exchanged twisted cubes. Frontiers of Computer Science 15, 3 (2021), 1–16.

Digital Library

[9]

Weibei Fan, Jianxi Fan, Cheng-Kuan Lin, Guijuan Wang, Baolei Cheng, and Ruchuan Wang. 2019. An efficient algorithm for embedding exchanged hypercubes into grids. The Journal of Supercomputing 75, 2 (2019), 783–807.

Digital Library

[10]

Wei-Bei Fan, Jian-Xi Fan, Cheng-Kuan Lin, Yan Wang, Yue-Juan Han, and Ru-Chuan Wang. 2019. Optimally embedding 3-ary n-cubes into grids. Journal of Computer Science and Technology 34, 2 (2019), 372–387.

[11]

Michael R Garey. 1979. A Guide to the Theory of NP-Completeness. Computers and intractability(1979).

[12]

Lawrence Hueston Harper. 2004. Global methods for combinatorial isoperimetric problems. Vol. 90. Cambridge University Press.

[13]

Howard P. Katseff. 1988. Incomplete hypercubes. IEEE transactions on computers 37, 5 (1988), 604–608.

Digital Library

[14]

Ville Leppänen, Martti Penttonen, and Martti Forsell. 2011. A layout for sparse cube-connected-cycles network. In Proceedings of the 12th International Conference on Computer Systems and Technologies. 32–37.

Digital Library

[15]

Paul Manuel, Indra Rajasingh, Bharati Rajan, and Helda Mercy. 2009. Exact wirelength of hypercubes on a grid. Discrete Applied Mathematics 157, 7 (2009), 1486–1495.

Digital Library

[16]

Koji Nakano. 2003. Linear layout of generalized hypercubes. International Journal of Foundations of Computer Science 14, 01(2003), 137–156.

[17]

Franco P Preparata and Jean Vuillemin. 1981. The cube-connected cycles: a versatile network for parallel computation. Commun. ACM 24, 5 (1981), 300–309.

Digital Library

[18]

Jingjing Xia, Yan Wang, Jianxi Fan, Weibei Fan, and Yuejuan Han. 2020. Embedding Augmented Cubes into Grid Networks for Minimum Wirelength.

Cited By

Vincy GRaj M(2024)Minimum linear arrangement and embedding of (K11 − C11)n into specific graphs with optimal wirelength calculationThe Journal of Supercomputing10.1007/s11227-024-06519-681:1Online publication date: 28-Nov-2024
https://doi.org/10.1007/s11227-024-06519-6
Angel DRevathi RNirmala MMallika M(2023)On M-Polynomials and Covering of Cube Connected Cycles2023 Third International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT)10.1109/ICAECT57570.2023.10117627(1-3)Online publication date: 5-Jan-2023
https://doi.org/10.1109/ICAECT57570.2023.10117627

Embedding Cube-Connected Cycles into Grid Network for Minimum Wirelength
1. Hardware
2. Mathematics of computing
  1. Discrete mathematics

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cover image ACM Conferences

WI-IAT '21: IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology

December 2021

541 pages

ISBN:9781450391870

DOI:10.1145/3498851

Copyright © 2021 ACM.

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Published: 11 April 2022

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WI-IAT '21: IEEE/WIC/ACM International Conference on Web Intelligence

December 14 - 17, 2021

VIC, Melbourne, Australia

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Cited By

Vincy GRaj M(2024)Minimum linear arrangement and embedding of (K11 − C11)n into specific graphs with optimal wirelength calculationThe Journal of Supercomputing10.1007/s11227-024-06519-681:1Online publication date: 28-Nov-2024
https://doi.org/10.1007/s11227-024-06519-6
Angel DRevathi RNirmala MMallika M(2023)On M-Polynomials and Covering of Cube Connected Cycles2023 Third International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT)10.1109/ICAECT57570.2023.10117627(1-3)Online publication date: 5-Jan-2023
https://doi.org/10.1109/ICAECT57570.2023.10117627

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