Let G be a directed graph. A vertex set F is called feedback vertex set (FVS) if its removal from G results in an acyclic graph. Because determining a minimum cardinality FVS is known to be NP hard, [Karp72], one is interested in designing fast approximation algorithms determining near-optimum FVSs. The paper presents deterministic and randomised heuristics based on Markov chains. In this regard, an earlier approximation algorithm developed in [Speckenmeyer89] is revisited and refined. Experimental results demonstrate the overall performance superiority of our algorithms compared to other algorithms known from literature with respect to both criteria, the sizes of solutions determined, as well as the consumed runtimes
