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On the parallel complexityof the alternating Hamiltonian cycle problem
Published online by Cambridge University Press: 15 August 2002
Abstract
Given a graph with colored edges, a Hamiltonian cycle is
called alternating if its successive edges differ in color. The problem
of finding such a cycle, even for 2-edge-colored graphs, is trivially
NP-complete, while it is known to be polynomial for 2-edge-colored
complete graphs. In this paper we study the parallel complexity of
finding such a cycle, if any, in 2-edge-colored complete graphs. We give
a new characterization for such a graph admitting an alternating
Hamiltonian cycle which allows us to derive a parallel algorithm for
the problem. Our parallel solution uses a perfect matching algorithm
putting the alternating Hamiltonian cycle problem to the RNC class. In
addition, a sequential version of our parallel algorithm improves the
computation time of the fastest known sequential algorithm for the
alternating Hamiltonian cycle problem by a factor of $O(\sqrt {n} )$.
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- © EDP Sciences, 1999