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IEICE Transactions on Information and Systems 2008 E91-D(4):1003-1009; doi:10.1093/ietisy/e91-d.4.1003
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Copyright © 2008 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Papers -- Algorithm Theory

The Container Problem in Bubble-Sort Graphs

Yasuto SUZUKI1 and Keiichi KANEKO1

1 The authors are with the Graduate School of Engineering, Tokyo University of Agriculture and Technology, Koganei-shi, 184–8588 Japan. E-mail: klkaneko{at}cc.tuat.ac.jp


  Abstract

Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

Key Words: bubble-sort graphs, internally disjoint paths, polynomial algorithm, fault tolerance

Manuscript received May 30, 2007. Manuscript revised October 12, 2007.


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