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- W4300694757 abstract "We show a close connection between structural hardness for $k$-partite graphs and tight inapproximability results for scheduling problems with precedence constraints. Assuming a natural but nontrivial generalisation of the bipartite structural hardness result of Bansal and Khot, we obtain a hardness of $2-epsilon$ for the problem of minimising the makespan for scheduling precedence-constrained jobs with preemption on identical parallel machines. This matches the best approximation guarantee for this problem. Assuming the same hypothesis, we also obtain a super constant inapproximability result for the problem of scheduling precedence-constrained jobs on related parallel machines, making progress towards settling an open question in both lists of ten open questions by Williamson and Shmoys, and by Schuurman and Woeginger. The study of structural hardness of $k$-partite graphs is of independent interest, as it captures the intrinsic hardness for a large family of scheduling problems. Other than the ones already mentioned, this generalisation also implies tight inapproximability to the problem of minimising the weighted completion time for precedence-constrained jobs on a single machine, and the problem of minimising the makespan of precedence-constrained jobs on identical parallel machine, and hence unifying the results of Bansal and Khot, and Svensson, respectively." @default.
- W4300694757 created "2022-10-04" @default.
- W4300694757 creator A5005843027 @default.
- W4300694757 creator A5061217984 @default.
- W4300694757 date "2015-07-07" @default.
- W4300694757 modified "2023-10-16" @default.
- W4300694757 title "Towards Tight Lower Bounds for Scheduling Problems" @default.
- W4300694757 doi "https://doi.org/10.48550/arxiv.1507.01906" @default.
- W4300694757 hasPublicationYear "2015" @default.
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