The geometry of scheduling

N. Bansal, K.R. Pruhs

Research output: Contribution to journalArticleAcademicpeer-review

28 Citations (Scopus)
78 Downloads (Pure)


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
Issue number5
Publication statusPublished - 2014


Dive into the research topics of 'The geometry of scheduling'. Together they form a unique fingerprint.

Cite this