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Embedding Cycles and Paths in Product Networks and Their Applications to Multiprocessor Systems
June 2012 (vol. 23 no. 6)
pp. 1081-1089
ASCII Text
x 
 
Tsong-Jie Lin, Sun-Yuan Hsieh, Justie Su-Tzu Juan, "Embedding Cycles and Paths in Product Networks and Their Applications to Multiprocessor Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 23, no. 6, pp. 1081-1089, June, 2012.
 
 
BibTex
x
 
@article{ 10.1109/TPDS.2011.245,
author = {Tsong-Jie Lin and Sun-Yuan Hsieh and Justie Su-Tzu Juan},
title = {Embedding Cycles and Paths in Product Networks and Their Applications to Multiprocessor Systems},
journal ={IEEE Transactions on Parallel and Distributed Systems},
volume = {23},
number = {6},
issn = {1045-9219},
year = {2012},
pages = {1081-1089},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPDS.2011.245},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Parallel and Distributed Systems
TI - Embedding Cycles and Paths in Product Networks and Their Applications to Multiprocessor Systems
IS - 6
SN - 1045-9219
SP1081
EP1089
EPD - 1081-1089
A1 - Tsong-Jie Lin,
A1 - Sun-Yuan Hsieh,
A1 - Justie Su-Tzu Juan,
PY - 2012
KW - Cartesian product networks
KW - cycle embedding
KW - generalized hypercubes
KW - nearest neighbor mesh hypercubes
KW - pancycle problem
KW - panconnectivity problem
KW - path embedding.
VL - 23
JA - IEEE Transactions on Parallel and Distributed Systems
ER -
 
Tsong-Jie Lin, Nan Jeon Institute of Technology, Tainan
Sun-Yuan Hsieh, National Cheng Kung University, Tainan
Justie Su-Tzu Juan, National Chi Nan University, Nantou
In this paper, we consider two embedding problems in Cartesian product networks: one is the pancycle problem, which involves embedding cycles of various lengths in the given product network; and the other is the panconnectivity problem, which involves embedding paths of various lengths between any pair of distinct nodes in the given product network. We then apply our technical lemmas and theorems to derive new topological properties of two multiprocessor systems, namely, generalized hypercubes and nearest neighbor mesh hypercubes.

[1] S.G. Akl, Parallel Computation: Models and Methods. Prentice Hall, 1997.
[2] B. Alspach and D. Hare, "Edge-Pancyclic Block-Intersection Graphs," Discrete Math., vol. 97, nos. 1-3, pp. 17-24, 1991.
[3] M. Anantha, B. Bose, and B. AlBdaiwi, "Mixed Radix Gray Codes," IEEE Trans. Computers, vol. 56, no. 10, pp. 1297-1307, Oct. 2007.
[4] M. Bae and B. Bose, "Edge Disjoint Hamiltonian Cycles in $k$ -Ary $n$ -Cube and Hypercubes," IEEE Trans. Computers, vol. 52, no. 10, pp. 1271-1284, Oct. 2003.
[5] L.N. Bhuyan and D.P. Agrawal, "Generalized Hypercube and Hyperbus Structures for a Computer Network," IEEE Trans. Computers, vol. C-33, no. 4, pp. 323-333, Apr. 1984.
[6] J.A. Bondy, "Pancyclic Graphs," J. Combinatorial Theory, Series B, vol. 11, no. 1, pp. 80-84, 1971.
[7] R.V. Boppana, S. Chalasani, and C.S. Raghavendra, "Resource Deadlock and Performance of Whormhole Multicast Routing Algorithms," IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 6, pp. 535-549, June 1998.
[8] V.V. Dimakopoulos, L. Palios, and A.S. Poulakidas, "On the Hamiltonicity of the Cartesian Product," Information Processing Letters, vol. 96, no. 2, pp. 49-53, 2005.
[9] S.Y. Hsieh and T.-J. Lin, "Panconnectivity and Edge-Pancyclicity of $k$ -Ary $n$ -Cubes," Networks, vol. 54, no. 1, pp. 1-11, 2009.
[10] R.E. Kessler and J.L. Schwarzmeier, "Cray T3D: A New Dimension for Cray Research," Proc. Compcon Spring '93, Digest of Papers, pp. 176-182, 1993.
[11] F.T. Leighton, Introduction to Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes. Morgan Kaufmann, 1992.
[12] X. Lin, P.K. Mckinley, and L.M. Ni, "Deadlock-Free Multicast Whormhole Routing in 2-D Mesh Multicomputers," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 8, pp. 793-804, Aug. 1994.
[13] W. Najjar and J.L. Gaudiot, "Network Resilience: A Measure of Network Fault Tolerance," IEEE Trans. Computers, vol. 39, no. 2, pp. 174-181, Feb. 1990.
[14] J.H. Park, "Panconnectivity and Edge-Pancyclicity of Faulty Recursive Circulant $G(2^m,4)$ ," Theoretical Computer Science, vol. 390, no. 1, pp. 70-80, 2008.
[15] Z.M. Song and Y.S. Qin, "A New Sufficient Condition for Panconnected Graphs," Ars Combinatoria, vol. 34, pp. 161-166, 1992.
[16] I.A. Stewart and Y. Xiang, "Bipanconnectivity and Bipancyclicity in $k$ -Ary $n$ -Cubes," IEEE Trans. Parallel and Distributed Systems, vol. 20, no. 1, pp. 25-33, Jan. 2009.
[17] D. Wang, T. An, M. Pan, K. Wang, and S. Qu, "Hamiltonian-Like Properties of $k$ -Ary $n$ -Cubes," Proc. Sixth Int'l Conf. Parallel and Distributed Computing, Applications and Technologies (PDCAT '05), pp. 1002-1007, 2005.
[18] N.C. Wang, C.P. Chu, and T.S. Chen, "A Dual-Hamiltonian-Path-Based Multicasting Strategy for Wormhole-Routed Star Graph Interconnection Networks," J. Parallel and Distributed Computing, vol. 62, no. 12, pp. 1747-1762, 2002.
[19] N.C. Wang, C.P. Yen, and C.P. Chu, "Multicast Communication in Wormhole-Routed Symmetric Networks with Hamiltonian Cycle Model," J. Systems Architecture, vol. 51, no. 3, pp. 165-183, 2005.
[20] J.M. Xu, Topological Structure and Analysis of Interconnection Networks. Kluwer Academic Publishers, 2001.
[21] J.M. Xu and M. Ma, "A Survey on Cycle and Path Embedding in Some Networks," Frontiers of Math. in China, vol. 4, no. 2, pp. 217-252, 2009.
[22] M. Xu, X.D. Hu, and J.M. Xu, "Edge-Pancyclicity and Hamiltonian Laceability of the Balanced Hypercubes," Applied Math. and Computation, vol. 189, no. 2, pp. 1393-1401, 2007.

Index Terms:
Cartesian product networks, cycle embedding, generalized hypercubes, nearest neighbor mesh hypercubes, pancycle problem, panconnectivity problem, path embedding.
Citation:
Tsong-Jie Lin, Sun-Yuan Hsieh, Justie Su-Tzu Juan, "Embedding Cycles and Paths in Product Networks and Their Applications to Multiprocessor Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 23, no. 6, pp. 1081-1089, June 2012, doi:10.1109/TPDS.2011.245
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