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IEICE Transactions on Information and Systems 2007 E90-D(4):716-721; doi:10.1093/ietisy/e90-d.4.716
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Copyright © 2007 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Papers -- Algorithm Theory

Hamiltonian Cycles and Hamiltonian Paths in Faulty Burnt Pancake Graphs

Keiichi KANEKO1

1 The author is with the Graduate School of Engineering, Tokyo University of Agriculture and Technology, Koganei-shi, 184-8588 Japan. E-mail: k1kaneko{at}cc.tuat.ac.jp


  Abstract

Recently, research on parallel processing systems is very active, and many complex topologies have been proposed. A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt pancake graph with degree n has a fault-free Hamiltonian cycle if the number of the faulty elements is n–2 or less, and it has a fault-free Hamiltonian path between any pair of nonfaulty nodes if the number of the faulty elements is n – 3 or less.

Key Words: signed permutation, interconnection network, routing algorithm, parallel processing

Manuscript received October 27, 2006.


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