Affiliation:
1. Max Planck Institute of Molecular Cell Biology and Genetics, Center for Systems Biology Dresden, Germany
2. Max Planck Institute of Molecular Cell Biology and Genetics, Center for Systems Biology Dresden and Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
Abstract
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, constant ratio approximations or proofs of inapproximability are unknown. We propose a new universal
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. Most of the relevant applications, such as
circuit testing
, ask for solving the FASP on large sparse graphs, which can be done efficiently within tight error bounds with our approach.
Publisher
Association for Computing Machinery (ACM)
Subject
Theoretical Computer Science
Cited by
4 articles.
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1. Finding small feedback arc sets on large graphs;Computers & Operations Research;2024-09
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4. Feedback Arc Set;Feedback Arc Set;2022