A Tabu search heuristic based on k-diamonds for the weighted feedback vertex set problem

Authors:
Francesco Carrabs;Raffaele Cerulli;Monica Gentili;Gennaro Parlato
Affiliations:
University of Salerno, Department of Mathematics;University of Salerno, Department of Mathematics;University of Salerno, Department of Computer Science;Liafa, CNRS and University Paris Diderot
Venue:
INOC'11 Proceedings of the 5th international conference on Network optimization
Year:
2011

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Abstract

Given an undirected and vertex weighted graph G = (V,E,w), the Weighted Feedback Vertex Problem (WFVP) consists of finding a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F. The WFVP on general graphs is known to be NP-hard and to be polynomially solvable on some special classes of graphs (e.g., interval graphs, co-comparability graphs, diamond graphs). In this paper we introduce an extension of diamond graphs, namely the k-diamond graphs, and give a dynamic programming algorithm to solve WFVP in linear time on this class of graphs. Other than solving an open question, this algorithm allows an efficient exploration of a neighborhood structure that can be defined by using such a class of graphs. We used this neighborhood structure inside our Iterated Tabu Search heuristic. Our extensive experimental results show the effectiveness of this heuristic in improving the solution provided by a 2-approximate algorithm for theWFVP on general graphs.