Combinatorial algorithms for feedback problems in directed graphs

Camil Demetrescu, Irene Finocchi
2003 Information Processing Letters  
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,
more » ... n terms of number of arcs, of a longest simple cycle of the digraph.
doi:10.1016/s0020-0190(02)00491-x fatcat:6hczz3tgo5f6tolcu4ge7c5rry