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Randomized on-line call control revisited

Leonardi, Stefano Alberto and Marchetti-Spaccamela, Alessio Presciutti

October 1997, 19 pages.

Status: available - back from printing

We consider the on-line problem of call admission and routing on trees and meshes. Previous work considered randomized algorithms and analyzed the {\em competitive ratio} of the algorithms. However, these previous algorithms could obtain very low profit with high probability. We investigate the question if it is possible to devise on-line competitive algorithms for these problems that would guarantee a ``good'' solution with ``good'' probability. We give a new family of randomized algorithms with provably optimal (up to constant factors) competitive ratios, and provably good probability to get a profit close to the expectation. We also give lower bounds that show bounds on how high the probability of such algorithms, to get a profit close to the expectation, can be. We also see this work as a first step towards understanding how well can the profit of an competitively-optimal randomized on-line algorithm be concentrated around its expectation.

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  AUTHOR = {Leonardi, Stefano Alberto and Marchetti-Spaccamela, Alessio Presciutti},
  TITLE = {Randomized on-line call control revisited},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-97-1-023},
  MONTH = {October},
  YEAR = {1997},
  ISSN = {0946-011X},