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The complexity of finding certain trees in tournaments

  • R. Balasubramanian
  • Venkatesh Raman
  • G. Srinivasaraghavan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 709)

Abstract

A tournament Tn is an orientation of the complete graph on n vertices. We continue the algorithmic study initiated by Hell and Rosenfeld[5] of recognizing various directed trees in tournaments. Hell and Rosenfeld considered orientations of paths, and showed the existence of oriented paths on n vertices finding which in Tn requires Θ(n lgα n) “edge probes” where α ≤ 1 is any fixed non-negative constant. Here, we investigate the complexity of finding a vertex of prescribed outdegree (or indegree). In particular, we show, by proving upper and lower bounds, that the complexity of finding a vertex of outdegree k(n−1)/2) in Tn is Θ(nk). We also establish an Ω(n2) lower bound for finding a vertex of maximum outdegree in Tn. These bounds are in sharp contrast to the O(n) bounds for selection in the case of transitive tournaments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • R. Balasubramanian
    • 1
  • Venkatesh Raman
    • 1
  • G. Srinivasaraghavan
    • 1
  1. 1.The Institute of Mathematical SciencesMadrasIndia

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