On the complexity of the Eulerian closed walk with precedence path constraints problem

Authors:
H. L. M. Kerivin;M. Lacroix;A. R. Mahjoub
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA;Université Blaise Pascal - Clermont-Ferrand II, LIMOS, CNRS UMR 6158, Complexe Scientifique des Cézeaux, 63177 Aubière Cedex, France;Université Blaise Pascal - Clermont-Ferrand II, LIMOS, CNRS UMR 6158, Complexe Scientifique des Cézeaux, 63177 Aubière Cedex, France
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

The Eulerian closed walk problem in a digraph is a well-known polynomial-time solvable problem. In this paper, we show that if we impose the feasible solutions to fulfill some precedence constraints specified by paths of the digraph, then the problem becomes NP-complete. We also present a polynomial-time algorithm to solve this variant of the Eulerian closed walk problem when the set of paths does not contain some forbidden structure. This allows us to give necessary and sufficient conditions for the existence of feasible solutions in this polynomial-time solvable case.