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Algorithms for finding maximum transitive subtournaments

Author

Listed:
  • Lasse Kiviluoto

    (Speago Ltd)

  • Patric R. J. Östergård

    (Aalto University School of Electrical Engineering)

  • Vesa P. Vaskelainen

    (Aalto University School of Electrical Engineering)

Abstract

The problem of finding a maximum clique is a fundamental problem for undirected graphs, and it is natural to ask whether there are analogous computational problems for directed graphs. Such a problem is that of finding a maximum transitive subtournament in a directed graph. A tournament is an orientation of a complete graph; it is transitive if the occurrence of the arcs $$xy$$ x y and $$yz$$ y z implies the occurrence of $$xz$$ x z . Searching for a maximum transitive subtournament in a directed graph $$D$$ D is equivalent to searching for a maximum induced acyclic subgraph in the complement of $$D$$ D , which in turn is computationally equivalent to searching for a minimum feedback vertex set in the complement of $$D$$ D . This paper discusses two backtrack algorithms and a Russian doll search algorithm for finding a maximum transitive subtournament, and reports experimental results of their performance.

Suggested Citation

  • Lasse Kiviluoto & Patric R. J. Östergård & Vesa P. Vaskelainen, 2016. "Algorithms for finding maximum transitive subtournaments," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 802-814, February.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9788-z
    DOI: 10.1007/s10878-014-9788-z
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    References listed on IDEAS

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    1. Butenko, S. & Wilhelm, W.E., 2006. "Clique-detection models in computational biochemistry and genomics," European Journal of Operational Research, Elsevier, vol. 173(1), pages 1-17, August.
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