Resource-sharing systems and hypergraph colorings

Wu-Hsiung Lin, Gerard J. Chang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A resource-sharing system is modeled by a hypergraph H in which a vertex represents a process and an edge represents a resource consisting of all vertices (processes) that have access to it. A schedule of H=(V,E) is a mapping f:ℕ→2 V, where f(i) is an independent set of H which consists of processes that operate at round i. The rate of f is defined as rate (f)=lim sup n→∞∑ n i=1|f(i)|/(n|V|) , which is the average fraction of operating processes at each round. The purpose of this paper is to study optimal rates for various classes of schedules under different fairness conditions. In particular, we give relations between these optimal rates and fractional/circular chromatic numbers. For the special case of the hypergraph is a connected graph, a new derivation for the previous result by Yeh and Zhu is also given.

Original languageEnglish
Pages (from-to)499-508
Number of pages10
JournalJournal of Combinatorial Optimization
Volume22
Issue number4
DOIs
StatePublished - 1 Nov 2011

Keywords

  • Circular chromatic number
  • Fractional chromatic number
  • Hypergraph
  • Resource-sharing system

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