Exact algorithms for a discrete metric labeling problem

Authors:
Arianna Alfieri;Gaia Nicosia;Andrea Pacifici
Affiliations:
Dipartimento di Sistemi di Produzione e Economia dell'Azienda, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy;Dipartimento di Informatica ed Automazione, Universití "Roma Tre", Via della Vasca Navale 79, I-00146 Roma, Italy;Dipartimento di Ingegneria dell'Impresa, Universití di Roma "Tor Vergata", via del Politecnico 1, I-00133 Roma, Italy
Venue:
Discrete Optimization
Year:
2006

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Abstract

We are given a edge-weighted undirected graph G=(V,E) and a set of labels/colors C={1,2,...,p}. A non-empty subset C"v@?C is associated with each vertex v@?V. A coloring of the vertices is feasible if each vertex v is colored with a color of C"v. A coloring uniquely defines a subset E^'@?E of edges having different colored endpoints. The problem of finding a feasible coloring which defines a minimum weight E^' is, in general, NP-hard. In this work we first propose polynomial time algorithms for some special cases, namely when the input graph is a tree, a cactus or with bounded tree-width. Then, an implicit enumeration scheme for finding an optimal coloring in the general case is described and computational results are presented.