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

Hervé Kerivin (1) , Mathieu Lacroix (2) , Ali Ridha Mahjoub (2)

1 Department of Mathematical Sciences [Clemson]
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

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.

Mots clés: Eulerian closed walk; Precedence path constraints; NP-completeness; Polynomial-time algorithm

Domaines: Informatique [cs]

Hervé Kerivin, Mathieu Lacroix, Ali Ridha Mahjoub. On the complexity of the Eulerian closed walk with precedence path constraints problem. Theoretical Computer Science, 2012, 439, ⟨10.1016/j.tcs.2012.03.014⟩. ⟨hal-01497107⟩