Constructing edge-disjoint spanning trees in product networks

IEEE Transactions on Parallel and Distributed Systems

Volumn 14, Issue 3, 2003, Pages 213-221

  Ku, Shan Chyun ^a   Wang, Biing Feng ^a   Hung, Ting Kai ^a  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

Cartesian product networks; Edge disjoint trees; Embedding; Fault tolerance; Interconnection networks; Spanning trees

Indexed keywords

ELECTRIC NETWORK TOPOLOGY; FAULT TOLERANT COMPUTER SYSTEMS; HAMILTONIANS; MATHEMATICAL TRANSFORMATIONS; PARALLEL ALGORITHMS; THEOREM PROVING; TREES (MATHEMATICS);

CARTESIAN PRODUCT NETWORK; EDGE-DISJOINT SPANNING TREE; SPANNING TREE;

INTERCONNECTION NETWORKS;

EID: 0037624721     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPDS.2003.1189580     Document Type: Article

References (21)

1. F. Bao, Y. Igarashi, and S.R. Öhring, "Reliable Broadcasting in Product Networks," Discrete Applied Math., vol. 83, pp. 3-20, 1998.
2. B. Barden, R. Libeskind-Hadas, J. Davis, and W. Williams, "On Edge-Disjoint Spanning Trees in Hypercubes," Information Processing Letters, vol. 70, pp. 13-16, 1999.
3. S. Bettayeb, "On the κ-ary Hypercube," Theoretical Computer Science, vol. 140, no. 2, pp. 333-339, 1995.
4. J.-C. Bermond, "Hamiltonian Decompositions of Graphs, Directed Graphs and Hypergraphs," Annals of Discrete Math., vol. 3, pp. 31-38, 1978.
5. S.K. Das, S.R. Öhring, and A.K. Banerjee, "Embeddings Into Hyper Petersen Network: Yet Another Hypercube-Like Interconnection Topology," VLSI Design, vol. 2, no. 4, pp. 335-351, 1995.
6. K. Day and A.-E. Al-Ayyoub, "The Cross Product of Interconnection Networks," IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 2, pp. 109-118, 1997.
7. V.V. Dimakopoulos and N.J. Dimopolulos, "A Theory for Total Exchange in Multidimensional Interconnection Networks," IEEE Trans. Parallel and Distributed Systems, vol. 9, no.7, pp. 639-649, 1998.
8. K. Efe and A. Fernandez, "Computational Properties of Mesh Connected Trees: Versatile Architecture for Parallel Computation," Proc. Int'l Conf. Parallel Processing, pp. 72-76, 1994.
9. A. Fernández and K. Efe, "Generalized Algorithm for Parallel Sorting on Product Networks," IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 12, pp. 1211-1225, 1997.
10. A. Fernández and K. Efe, "Efficient VLSI Layouts for Homogeneous Product Networks," IEEE Trans. Computers, vol. 46, no. 10, pp. 1070-1082, 1997.
11. P. Fragopoulou and S.G. Akl, "Edge-Disjoint Spanning Trees on the Star Network with Applications to Fault Tolerance," IEEE Trans. Computers, vol. 45, no. 2, pp. 174-185, 1996.
12. P. Fragopoulou, P.S.G. Akl, and H. Meijer, "Optimal Communication Primitives on the Generalized Hypercube Network," J. Parallel and Distributed Computing, vol. 32, no. 2, pp. 173-187, 1996.
13. F. Harary, "On the Group of the Composition of Two Graphs," Duke Math. J., vol. 26, 1959.
14. T. Hasunuma, "On Edge-Disjoint Spanning Trees With Small Depths," Information Processing Letters, vol. 75, pp. 71-74, 2000.
15. A. Itai and M. Rodeh, "The Multi-Tree Approach to Reliability in Distributed Networks," Information and Computation, vol. 79, pp. 43-59, 1988.
16. S.L. Johnsson and C.T. Ho, "Optimum Broadcasting and Personalized Communication in Hypercubes," IEEE Trans. Computers, vol. 38, no. 9, pp. 1249-1268, 1989.
17. R. Libeskind-Hadas, D. Mazzoni, and R. Rajagopalan, "Tree-Based Multicasting in Wormhole-Routed Irregular Topologies," Proc. Merged 12th Int'l Parallel Processing Symp. and the Ninth Symp. Parallel and Distributed Processing, pp. 244-249, Apr. 1998.
18. G. Sabidussi, "The Composition of Graphs," Duke Math. J., vol. 26, pp. 693-696, 1959.
19. R. Stong, "Hamilton Decompositions of Cartesian Products of Graphs," Discrete Math., vol. 90, pp. 169-190, 1991.
20. J. Roskind and R. Tarjan, "A Note on Finding Maximum-Cost Edge-Disjoint Spanning Trees," Math. Operations Research, vol. 10, no. 2, pp. 701-708, Nov. 1985.
21. H. Wang and D. Blough, "Construction of Edge-Disjoint Spanning Trees in the Torus and Application to Multicast in Wormhole-Routed Networks," Proc. Int'l Conf. Parallel and Distributed Computing Systems, 1999.