Online capacitated interval coloring

Leah Epstein, Thomas Erlebach, Asaf Levin

Research output: Contribution to journalArticlepeer-review

Abstract

In the online capacitated interval coloring problem, a sequence of requests arrive online. Each request is an interval Ij ⊆ {1, 2, ⋯, n} with bandwidth bj. We are initially given a vector of capacities (c1, c2, ⋯, cn). Each color can support a set of requests such that the total bandwidth of intervals containing i is at most ci. The goal is to color the requests using a minimum number of colors. We present a constant competitive algorithm for the case where the maximum bandwidth bmax = maxj bj is at most the minimum capacity cmin = mini c i. For the case bmax > cmin, we give an algorithm with competitive ratio O(log bmax/cmin) and, using resource augmentation, a constant competitive algorithm. We also give a lower bound showing that a constant competitive ratio cannot be achieved in the general case without resource augmentation.

Original languageEnglish
Pages (from-to)822-841
Number of pages20
JournalSIAM Journal on Discrete Mathematics
Volume23
Issue number2
DOIs
StatePublished - 2009

Keywords

  • Competitive analysis
  • Interval coloring with bandwidth
  • Lower bound

ASJC Scopus subject areas

  • Mathematics (all)

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