Papers › Tight Localizations of Feedback Sets
Tight Localizations of Feedback Sets
Michael Hecht, Krzysztof Gonciarz, Szabolcs Horvát
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The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs ε⊆E or vertices ν⊆V whose removal G∖ε, G∖ν makes a given multi-digraph G=(V,E) acyclic, respectively. Though both problems are known to be APX-hard, approximation algorithms or proofs of inapproximability are unknown. We propose a new 𝒪(|V||E|⁴)-heuristic for the directed FASP. While a ratio of r ≈1.3606 is known to be a lower bound for the APX-hardness, at least by empirical validation we achieve an approximation of r ≤2. The most relevant applications, such as circuit testing, ask for solving the FASP on large sparse graphs, which can be done efficiently within tight error bounds due to our approach.
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