Online function tracking with generalized penalties

  • Authors:
  • Marcin Bienkowski;Stefan Schmid

  • Affiliations:
  • Institute of Computer Science, University of Wrocław, Poland;Deutsche Telekom Laboratories, TU Berlin, Germany

  • Venue:
  • SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
  • Year:
  • 2010

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Abstract

We attend to the classic setting where an observer needs to inform a tracker about an arbitrary time varying function f: ℕ0 →ℤ. This is an optimization problem, where both wrong values at the tracker and sending updates entail a certain cost. We consider an online variant of this problem, i.e., at time t, the observer only knows f(t′) for all t′≤t. In this paper, we generalize existing cost models (with an emphasis on concave and convex penalties) and present two online algorithms. Our analysis shows that these algorithms perform well in a large class of models, and are even optimal in some settings.