An Equivalent Version of the Caccetta-Häggkvist Conjecture in an Online Load Balancing Problem

  • Angelo Monti
  • Paolo Penna
  • Riccardo Silvestri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4769)

Abstract

We study the competitive ratio of certain online algorithms for a well-studied class of load balancing problems. These algorithms are obtained and analyzed according to a method by Crescenzi et al (2004). We show that an exact analysis of their competitive ratio on certain “uniform” instances would resolve a fundamental conjecture by Caccetta and Häggkvist (1978). The conjecture is that any digraph on n nodes and minimum outdegree d must contain a directed cycle involving at most ⌈n/d ⌉ nodes. Our results are the first relating this conjecture to the competitive analysis of certain algorithms, thus suggesting a new approach to the conjecture itself. We also prove that, on “uniform” instances, the analysis by Crescenzi et al (2004) gives only trivial upper bounds, unless we find a counterexample to the conjecture. This is in contrast with other (notable) examples where the same analysis yields optimal (non-trivial) bounds.

Keywords

Caccetta-Häggkvist conjecture online load balancing competitive analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Angelo Monti
    • 1
  • Paolo Penna
    • 2
  • Riccardo Silvestri
    • 1
  1. 1.Dipartimento di Informatica, Università degli Studi di Roma “La Sapienza”, via Salaria 113, RomaItaly
  2. 2.Dipartimento di Informatica ed Applicazioni “R.M. Capocelli”, Università di Salerno, via S. Allende 2, Baronissi (SA)Italy

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