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On the parallel complexityof the alternating Hamiltonian cycle problem

Published online by Cambridge University Press:  15 August 2002

E. Bampis
Affiliation:
LaMI, Université d'Evry-Val-d'Essonne, 91025 Evry Cedex, France.
Y. Manoussakis
Affiliation:
L.R.I., bâtiment 490, Université de Paris-Sud, 91405 Orsay Cedex, France.
I. Milis
Affiliation:
L.R.I., bâtiment 490, Université de Paris-Sud, 91405 Orsay Cedex, France.
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Abstract

Given a graph with colored edges, a Hamiltonian cycle iscalled alternating if its successive edges differ in color. The problemof finding such a cycle, even for 2-edge-colored graphs, is triviallyNP-complete, while it is known to be polynomial for 2-edge-coloredcomplete graphs. In this paper we study the parallel complexity of finding such a cycle, if any, in 2-edge-colored complete graphs. We givea new characterization for such a graph admitting an alternatingHamiltonian cycle which allows us to derive a parallel algorithm forthe problem. Our parallel solution uses a perfect matching algorithmputting the alternating Hamiltonian cycle problem to the RNC class. Inaddition, a sequential version of our parallel algorithm improves thecomputation time of the fastest known sequential algorithm for thealternating Hamiltonian cycle problem by a factor of $O(\sqrt {n} )$ .

Type
Research Article
Copyright
© EDP Sciences, 1999

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