Probabilistic Analysis of Online Bin Coloring Algorithms Via Stochastic Comparison

  • Authors:

  • Benjamin Hiller;Tjark Vredeveld

  • Affiliations:

  • Zuse Institute Berlin, Berlin, Germany D---14195;Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands 6200 MD

  • Venue:
  • ESA '08 Proceedings of the 16th annual European symposium on Algorithms
  • Year:
  • 2008

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Abstract

This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced in [15]. Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm $\textsc{GreedyFit}$ is stochastically better than the performance of the algorithm $\textsc{OneBin}$ for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.