The geometry of scheduling

N. Bansal, K.R. Pruhs

Research output: Contribution to journalArticleAcademicpeer-review

25 Citations (Scopus)
48 Downloads (Pure)

Abstract

We consider the following general scheduling problem. The input consists of $n$ jobs, each with an arbitrary release time, size, and monotone function specifying the cost incurred when the job is completed at a particular time. The objective is to find a preemptive schedule of minimum aggregate cost. This problem formulation is general enough to include many natural scheduling objectives, such as total weighted flow time, total weighted tardiness, and sum of flow time squared. We give an $O(\log \log P )$ approximation for this problem, where $P$ is the ratio of the maximum to minimum job size. We also give an $O(1)$ approximation in the special case of identical release times. These results are obtained by reducing the scheduling problem to a geometric capacitated set cover problem in two dimensions.
Original languageEnglish
Pages (from-to)1684-1698
JournalSIAM Journal on Computing
Volume43
Issue number5
DOIs
Publication statusPublished - 2014

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