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

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Brüggemann, Tobias and Monnot, Jérôme and Woeginger, Gerhard J. (2003) Local search for the minimum label spanning tree problem with bounded color classes. Operations Research Letters (3). pp. 195-201. ISSN 0167-6377

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Abstract: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- and APX-complete for any fixed r3.

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 k3, there exist instances for which some local optima are a factor of r/2 away from the global optimum.
Item Type:Article
Copyright:© 2003 Elsevier
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/75016
Official URL:http://dx.doi.org/10.1016/S0167-6377(02)00241-9
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