A linear time algorithm for the minimum Weighted Feedback Vertex Set on diamonds

Authors:
F. Carrabs;R. Cerulli;M. Gentili;G. Parlato
Affiliations:
Dipartimento di Matematica ed Informatica, Università di Salerno, 84084 Fisciano (SA), Italy;Dipartimento di Matematica ed Informatica, Università di Salerno, 84084 Fisciano (SA), Italy;Dipartimento di Matematica ed Informatica, Università di Salerno, 84084 Fisciano (SA), Italy;Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy
Venue:
Information Processing Letters
Year:
2005

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Abstract

Given an undirected and vertex weighted graph G, the Weighted Feedback Vertex Problem (WFVP) consists in 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. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to solve WFVP on it.