Online set packing

Yuval Emekj, Magnús M. Halldórsson, Yishay Mansour, Boaz Patt-Shamir, Jaikumar Radhakrishnan, Dror Rawitz

Research output: Contribution to journalArticlepeer-review

Abstract

In online set packing (OSP), elements arrive online, announcing which sets they belong to, and the algorithm needs to assign each element, upon arrival, to one of its sets. The goal is to maximize the number of sets that are assigned all their elements: a set that misses even a single element is deemed worthless. This is a natural online optimization problem that abstracts allocation of scarce compound resources, e.g., multipacket data frames in communication networks. We present a randomized competitive online algorithm for the weighted case with general capacity (namely, where sets may have different values, and elements arrive with different multiplicities). We prove a matching lower bound on the competitive ratio for any randomized online algorithm. Our bounds are expressed in terms of the maximum set size and the maximum number of sets an element belongs to. We also present refined bounds that depend on the uniformity of these parameters.

Original languageEnglish
Pages (from-to)728-746
Number of pages19
JournalSIAM Journal on Computing
Volume41
Issue number4
DOIs
StatePublished - 2012

Keywords

  • Competitive analysis
  • Multipacket frames
  • Online set packing
  • Packet fragmentation
  • Randomized algorithm

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