The problem of the moody chess players

  • Authors:

  • Fokko J. van de Bult;Gerhard J. Woeginger

  • Affiliations:

  • Korteweg--de Vries Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands;Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

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Abstract

We analyze a sorting problem where for every element there is a hard upper bound on the overall number of lost comparisons: Given are n elements and n non-negative integers a"1,...,a"n. The goal is to sort these n elements by pairwise comparisons, subject to the condition that the kth element must not be the loser (= smaller element) in more than a"k of its comparisons against the other elements. We completely characterize the sequences a"1,...,a"n for which this sorting problem can be solved.