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The shortest routing path in star graphs with faulty clusters

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2 Author(s)
Qian-Ping Gu ; Dept. of Comput. Software, Aizu Univ., Japan ; Shientung Peng

Given a graph G, a cluster C is a connected subgraph of G, and C is called a faulty cluster if all nodes in C are faulty. Given an n-dimensional star graph Gn with n-2 faulty clusters of diameter at most 2, it has been shown by the authors (1994) that any two non-faulty nodes s and t of Gn can be connected by a fault-free path of length at most d(Gn)+6 in O(n2) time, where d(Gn)=[(3(n-1))/2] is the diameter of Gn . In this paper, we prove that a fault-free path s→t of length at most d(Gn)+1 if n>10 or n is odd, or d(Gn )+2 otherwise, can be found in O(n2) time. The length of the path s→t is optimal

Published in:

Parallel Algorithms/Architecture Synthesis, 1997. Proceedings., Second Aizu International Symposium

Date of Conference:

17-21 Mar 1997