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 program- ming 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 neigh- borhood structure that can be defined by using such a class of graphs. We used this neighborhood structure inside our Iterated Tabu Search heuristic. Our exten- sive experimental results show the effectiveness of this heuristic in improving the solution provided by a 2-approximate algorithm for the WFVP on general graphs.
A Tabu Search Heuristic Based on k-Diamonds for the Weighted Feedback Vertex Set Problem
CARRABS, FRANCESCO;CERULLI, Raffaele;GENTILI, Monica;
2011-01-01
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 program- ming 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 neigh- borhood structure that can be defined by using such a class of graphs. We used this neighborhood structure inside our Iterated Tabu Search heuristic. Our exten- sive experimental results show the effectiveness of this heuristic in improving the solution provided by a 2-approximate algorithm for the WFVP on general graphs.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
