Online Function Tracking with Generalized Penalties

  • Marcin Bienkowski
  • Stefan Schmid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6139)


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.


Penalty Function Input Sequence Competitive Ratio Online Algorithm Total Penalty 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marcin Bienkowski
    • 1
  • Stefan Schmid
    • 2
  1. 1.Institute of Computer ScienceUniversity of WrocławPoland
  2. 2.Deutsche Telekom LaboratoriesTU BerlinGermany

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