Node-to-set disjoint paths problem in bi-rotator graphs

Abstract

A rotator graph was proposed as a topology for interconnection networks of parallel computers, and it is promising because of its small diameter and small degree. However, a rotator graph is a directed graph that sometimes behaves harmful when it is applied to actual problems. A bi-rotator graph is obtained by making each edge of a rotator graph bi-directional. A bi-rotator has a Hamilton cycle and it is also pan-cyclic. In this paper, we give an algorithm for the node-to-set disjoint paths problem in bi-rotator graphs with its evaluation results. The solution achieves some fault tolerance such as file distribution based information dispersal technique. The algorithm is of polynomial order of n for an n-bi-rotator graph. It is based on recursion and divided into three cases according to the distribution of destination nodes in classes into which all the nodes in a bi-rotator graph are categorized. The sum of lengths of paths obtained and the time complexity of the algorithm are estimated. Average performance of the algorithm is also evaluated by computer experiments. © Springer-Verlag Berlin Heidelberg 2004.