Local search for the minimum label spanning tree problem with bounded color classes

Tobias Brüggemann (1) , Jérôme Monnot (2) , Gerhard J. Woeginger (1)

1 Department of Mathematics, University of Twente
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

In the Minimum Label Spanning Tree problem, the input consists of an edge-colored undirected graph, and the goal is to find a spanning tree with the minimum number of different colors. We investigate the special case where every color appears at most r times in the input graph. This special case is polynomially solvable for r=2, and NP-complete and APX-complete for any fixed r>2. We analyze local search algorithms that are allowed to switch up to k of the colors used in a feasible solution. We show that for k=2 any local optimum yields an (r+1)/2-approximation of the global optimum, and that this bound is tight. For every k>2, there exist instances for which some local optima are a factor of r/2 away from the global optimum.

Mots clés: Graph algorithms; approximation algorithms; combinatorial optimization; local search; complexity; APX-completeness

Domaines: Mathématique discrète [cs.DM]

Tobias Brüggemann, Jérôme Monnot, Gerhard J. Woeginger. Local search for the minimum label spanning tree problem with bounded color classes. Operations Research Letters, 2003, 31, pp.195-201. ⟨hal-00004062⟩