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Resource-sharing systems and hypergraph colorings

Author

Listed:
  • Wu-Hsiung Lin

    (National Taiwan University)

  • Gerard J. Chang

    (National Taiwan University
    National Taiwan University
    National Center for Theoretical Sciences, Taipei Office)

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 ${\rm rate}(f)=\limsup_{n\to\infty}\sum_{i=1}^{n}|f(i)|/(n|V|)$ , 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.

Suggested Citation

  • Wu-Hsiung Lin & Gerard J. Chang, 2011. "Resource-sharing systems and hypergraph colorings," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 499-508, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9295-9
    DOI: 10.1007/s10878-010-9295-9
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    1. Strolin-Goltzman, Jessica & Ura, Sarah & Bielawski-Branch, Amy & Hill, Michael & Kim, Rhiannon & Bleau, Tina & Jorgenson, Jennifer & Meierdiercks, Erika & Hazen, Andrea & Conradi, Lisa & Forehand, Rex, 2023. "Feasibility of the NCTSN breakthrough parenting curriculum: A pilot study of an online trauma-informed training for birth parents involved in the child welfare system," Children and Youth Services Review, Elsevier, vol. 150(C).

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