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→2V, 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
