Optimal fault-tolerant linear arrays

Authors:
Toshinori Yamada;Shuichi Ueno
Affiliations:
Saitama University, Saitama, Japan;Tokyo Institute of Technology, Tokyo, Japan
Venue:
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Year:
2003

Citing 6
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Abstract

This paper proves that for every positive integers n and k, we can explicitly construct a graph G with n+O(k) vertices and maximum degree 3, such that even after removing any k vertices from G, the remaining graph still contains a path of length n-1. This settles a problem raised by Zhang [11, 12] in connection with the design of fault-tolerant linear arrays.