Algorithms for finding maximum transitive subtournaments

Lasse Kiviluoto, Patric R. J. Östergård () and Vesa P. Vaskelainen
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Lasse Kiviluoto: Speago Ltd
Patric R. J. Östergård: Aalto University School of Electrical Engineering
Vesa P. Vaskelainen: Aalto University School of Electrical Engineering

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 21, 802-814

Abstract: 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.

Keywords: Backtrack search; Clique; Directed acyclic graph; Feedback vertex set; Russian doll search; Transitive tournament (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9788-z

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