Efficient heuristics to compute minimal and stable feedback arc sets

Given a directed graph G = ( V , A ) , we tackle the Minimum Feedback Arc Set (MFAS) Problem by designing an efficient algorithm to search for minimal and stable Feedback Arc Sets, i.e. such that none of the arcs can be reintroduced in the graph without disrupting acyclicity and such that for each v...

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 48; no. 4
Main Authors Cavallaro, Claudia, Cutello, Vincenzo, Pavone, Mario
Format Journal Article
LanguageEnglish
Published New York Springer US 2024
Springer Nature B.V
Subjects
Algorithms
Combinatorics
Convex and Discrete Geometry
Feedback
Graph theory
Graphs
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Theory of Computation
Upper bounds
Linear arrangement of vertices
Heuristics
Experimental analysis
Optimization problem
Minimal feedback arc set
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Summary:Given a directed graph G = ( V , A ) , we tackle the Minimum Feedback Arc Set (MFAS) Problem by designing an efficient algorithm to search for minimal and stable Feedback Arc Sets, i.e. such that none of the arcs can be reintroduced in the graph without disrupting acyclicity and such that for each vertex the number of eliminated outgoing (resp. incoming) arcs is not bigger than the number of remaining incoming (resp. outgoing) arcs. Our algorithm has a good polynomial upper bound and can therefore be applied even on large graphs. We also introduce an algorithm to generate strongly connected graphs with a known upper bound on their feedback arc set, and on such graphs we test our algorithm.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-024-01209-8