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Maximal and Maximum Transitive Relation Contained in a Given Binary Relation

  • Sourav Chakraborty
  • Shamik Ghosh
  • Nitesh JhaEmail author
  • Sasanka Roy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9198)

Abstract

We study the problem of finding a maximal transitive relation contained in a given binary relation. Given a binary relation of size m defined on a set of size n, we present a polynomial time algorithm that finds a maximal transitive sub-relation in time \(O(n^2 + nm)\).

We also study the problem of finding a maximum transitive relation contained in a binary relation. For the class of triangle-free relations (directed graphs), we present a 0.874-approximation via the problem of maximum directed cut.

Keywords

Directed Graph Binary Relation Transitive Closure Transitive Relation Transitive Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sourav Chakraborty
    • 1
  • Shamik Ghosh
    • 2
  • Nitesh Jha
    • 1
    Email author
  • Sasanka Roy
    • 1
  1. 1.Chennai Mathematical InstituteChennaiIndia
  2. 2.Department of MathematicsJadavpur UniversityKolkataIndia

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