The complexity of the Pk partition problem and related problems in bipartite graphs

Jérôme Monnot (1) , Sophie Toulouse (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 LIPN - Laboratoire d'Informatique de Paris-Nord

In this paper, we continue the investigation made in [MT05] about the approximability of Pk partition problems, but focusing here on their complexity. Precisely, we aim at designing the frontier between polynomial and NP-complete versions of the Pk partition problem in bipartite graphs, according to both the constant k and the maximum degree of the input graph. We actually extend the obtained results to more general classes of problems, namely, the minimum k-path partition problem and the maximum Pk packing problem. Moreover, we propose some simple approximation algorithms for those problems.

Mots clés: Pk-partition; maximum (weighted) Pk-packing; minimum k-path partition; bipartite graphs; NP-completeness; approximation algorithms

Domaines: Complexité [cs.CC]; Mathématique discrète [cs.DM]

Jérôme Monnot, Sophie Toulouse. The complexity of the Pk partition problem and related problems in bipartite graphs. Theory and Practice of Computer Science, 2007, pp.422-433. ⟨hal-00152314⟩