Variable sized online interval coloring with bandwidth

  • Authors:

  • Leah Epstein;Thomas Erlebach;Asaf Levin

  • Affiliations:

  • Department of Mathematics, University of Haifa, Haifa, Israel;Department of Computer Science, University of Leicester, Leicester, United Kingdom;Department of Statistics, The Hebrew University, Jerusalem, Israel

  • Venue:
  • SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
  • Year:
  • 2006

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Abstract

We consider online coloring of intervals with bandwidth in a setting where colors have variable capacities. Whenever the algorithm opens a new color, it must choose the capacity for that color and cannot change it later. The goal is to minimize the total capacity of all the colors used. We consider the bounded model, where all capacities must be chosen in the range (0,1], and the unbounded model, where the algorithm may use colors of any positive capacity. For the absolute competitive ratio, we give an upper bound of 14 and a lower bound of 4.59 for the bounded model, and an upper bound of 4 and a matching lower bound of 4 for the unbounded model. We also consider the offline version of these problems and show that the unbounded model is polynomially solvable, while the bounded model is NP-hard in the strong sense and admits a 3.6-approximation algorithm