The problem of the moody chess players

We analyze a sorting problem where for every element there is a hard tipper bound on the overall number of lost comparisons: Given are n elements and n [ion-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. (c) 2008 Elsevier B.V. All rights reserved.