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Efficient heuristics to compute minimal and stable feedback arc sets

Author

Listed:
  • Claudia Cavallaro

    (University of Catania)

  • Vincenzo Cutello

    (University of Catania)

  • Mario Pavone

    (University of Catania)

Abstract

Given a directed graph $$G=(V,A)$$ 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.

Suggested Citation

  • Claudia Cavallaro & Vincenzo Cutello & Mario Pavone, 2024. "Efficient heuristics to compute minimal and stable feedback arc sets," Journal of Combinatorial Optimization, Springer, vol. 48(4), pages 1-24, November.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:4:d:10.1007_s10878-024-01209-8
    DOI: 10.1007/s10878-024-01209-8
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