Combinatorial algorithms for feedback problems in directed graphs

Authors:
Camil Demetrescu;Irene Finocchi
Affiliations:
Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma "La Sapienza", Via Salaria 113, 00198 Roma, Italy;Dipartimento di Informatica, Sistemi e Produzione, Università degli Studi di Roma "Tor Vergata", Via di Tor Vergata 110, 00133 Roma, Italy
Venue:
Information Processing Letters
Year:
2003

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Abstract

Given a weighted directed graph G = (V, A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A' ⊆ A such that the directed graph (V, A \ A') is acyclic. Similarly, the minimum feedback vertex set problem consists of finding a minimum weight set of vertices containing at least one vertex for each directed cycle. Both problems are NP-complete. We present simple combinatorial algorithms for these problems that achieve an approximation ratio bounded by the length, in terms of number of arcs, of a longest simple cycle of the digraph.