k-Pairwise Cluster Fault Tolerant Routing in Hypercubes

Qian-Ping Gu; Shietung Peng

doi:10.1109/12.620486

Publication
1997
Issue No. 9 - September
Abstract - k-Pairwise Cluster Fault Tolerant Routing in Hypercubes

	This Article
	Subscribers, please Login Purchase article: $19 PDF HTML IEEE Xplore Subscribers RSS feed
	Share
	Email this Article to a friend
	Bibliographic References
	ASCII Text BibTex RefWorks Procite/RefMan/EndNote
	Add to:
	Digg Furl Spurl Blink Simpy Google Del.icio.us Y!MyWeb
	Search
	Similar Articles Articles by Qian-Ping Gu Articles by Shietung Peng

k-Pairwise Cluster Fault Tolerant Routing in Hypercubes

September 1997 (vol. 46 no. 9)

pp. 1042-1049

	ASCII Text	x
	Qian-Ping Gu, Shietung Peng, "k-Pairwise Cluster Fault Tolerant Routing in Hypercubes," IEEE Transactions on Computers, vol. 46, no. 9, pp. 1042-1049, September, 1997.

	BibTex	x
	@article{ 10.1109/12.620486, author = {Qian-Ping Gu and Shietung Peng}, title = {k-Pairwise Cluster Fault Tolerant Routing in Hypercubes}, journal ={IEEE Transactions on Computers}, volume = {46}, number = {9}, issn = {0018-9340}, year = {1997}, pages = {1042-1049}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.620486}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - JOUR JO - IEEE Transactions on Computers TI - k-Pairwise Cluster Fault Tolerant Routing in Hypercubes IS - 9 SN - 0018-9340 SP1042 EP1049 EPD - 1042-1049 A1 - Qian-Ping Gu, A1 - Shietung Peng, PY - 1997 KW - Interconnection networks KW - algorithms KW - node-disjoint paths KW - node fault tolerant routing. VL - 46 JA - IEEE Transactions on Computers ER -

Qian-Ping Gu

Shietung Peng

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.620486

Abstract—In this paper, we introduce a general fault tolerant routing problem, cluster fault tolerant routing, which is a natural extension of the well studied node fault tolerant routing problem. A cluster is a connected subgraph of a graph G, and a cluster is faulty if all nodes in it are faulty. In cluster fault tolerant routing (abbreviated as CFT routing), we are interested in the number of faulty clusters and the size of the clusters that an interconnection network can tolerate for certain routing problems. As a case study, we investigate the following k-pairwise CFT routing in n-dimensional hypercubes H_n: Given a set of faulty clusters and k distinct nonfaulty node pairs (s₁, t₁), ..., (s_k, t_k) in H_n, find k fault-free node-disjoint paths s_i→t_i, 1 ≤i≤k. We show that H_n can tolerate n− 2 faulty clusters of diameter one, plus one faulty node for the k-pairwise CFT routing with k = 1. For n≥ 4 and $2 \le k \le \lceil n/2 \rceil,$ we prove that H_n can tolerate n− 2k + 1 faulty clusters of diameter one for the k-pairwise CFT routing. We also give an O(kn log n) time algorithm which finds the k paths for the mentioned problem. Our algorithm implies an O(n2 log n) time algorithm for the k-pairwise node-disjoint paths problem in H_n, which improves the previous result of O(n3 log n).

[1] J.C. Bermond, "Interconnection Networks," Discrete Applied Math, special issue, 1992.
[2] A.H. Esfahanian, “Generalized Measures of Fault Tolerance with Application to n-Cube Networks,” IEEE Trans. Computers, vol. 38, no. 11, pp. 1,586-1,591, 1989.
[3] Q. Gu and S. Peng, "An Efficient Algorithm for Node-to-Node Routing in Hypercubes with Faulty Clusters," Computer J., vol. 39, no. 1, pp. 14-19, 1996.
[4] D.F. Hsu, "Interconnection Networks and Algorithms," Networks, special issue, vol. 23, no. 4, 1993.
[5] D.F. Hsu, "On Container With Width and Length in Graphs, Groups, and Networks," IEICE Trans. Fundamental of Electronics, Information, and Computer Sciences, vol. E77-A, no. 4, pp. 668-680, 1994.
[6] D.F. Hsu and Y.O. Lyuu, "A Graph Theoretical Study of Transmission Delay and Fault Tolerance," Proc. Fourth ISMM Int'l Conf. Parallel and Distributed Computing and Systems, pp. 20-24, 1991.
[7] R.M. Karp, "On the Computational Complexity of Combinational Problems," Networks, vol. 5, pp. 45-68, 1975.
[8] S. Latifi, “Combinatorial Analysis of the Fault Diameter of the$n$-Cube,” IEEE Trans. Computers, vol. 42, no.1, pp. 27-33, 1993.
[9] S. Madhavapeddy and I.H. Sudborough, "A Topological Property of Hypercubes: Node Disjoint Paths," Proc. Second IEEE Symp. Parallel and Distributed Processing, pp. 532-539, 1990.
[10] J. McHugh, Algorithmic Graph Theory. Prentice Hall, 1990.
[11] M.O. Rabin, Efficient Dispersal of Information for Security, Load Balancing and Fault Tolerance J. ACM, vol. 36, no. 2, pp. 335-348, 1989.
[12] Y. Saad and M. Schultz, "Topological Properties of Hypercubes," IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988.
[13] C. L. Seitz,“The cosmic cube,”CACM, vol. 28, pp. 22–33, Jan. 1985.
[14] Y. Shiloach, "The Two Paths Problem Is Polynomial," Technical Report STAN-CS-78-654, Stanford Univ., 1978.
[15] S.-B. Tien and C.S. Raghavendra,“Algorithms and bounds for shortest paths and diameter in faultyhypercubes,” IEEE Trans. Parallel and Distributed Systems, pp. 713-718, June 1993.
[16] M. Watkin, "On the Existence of Certain Disjoint Arcs in Graphs," Duke Math. J., 1968.

Index Terms:

Interconnection networks, algorithms, node-disjoint paths, node fault tolerant routing.

Citation:

Qian-Ping Gu, Shietung Peng, "k-Pairwise Cluster Fault Tolerant Routing in Hypercubes," IEEE Transactions on Computers, vol. 46, no. 9, pp. 1042-1049, Sept. 1997, doi:10.1109/12.620486

Peer Review Notice | Give Us Feedback

Usage of this product signifies your acceptance of the Terms of Use.