NDLI: Unrelated machine scheduling of jobs with uniform smith ratios

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Unrelated machine scheduling of jobs with uniform smith ratios

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Unrelated machine scheduling of jobs with uniform smith ratios

Content Provider	ACM Digital Library
Author	Kalaitzis, Christos Tarnawski, Jakub Svensson, Ola
Abstract	We consider the classic problem of scheduling jobs on unrelated machines so as to minimize the weighted sum of completion times. Recently, for a small constant ε > 0, Bansal et al. gave a (3/2 ™ ε)-approximation algorithm improving upon the "natural" barrier of 3/2 which follows from independent randomized rounding. In simplified terms, their result is obtained by an enhancement of independent randomized rounding via strong negative correlation properties. In this work, we take a different approach and propose to use the same elegant rounding scheme for the weighted completion time objective as devised by Shmoys and Tardos for optimizing a linear function subject to makespan constraints. Our main result is a 1.21-approximation algorithm for the natural special case where the weight of a job is proportional to its processing time (specifically, all jobs have the same Smith ratio), which expresses the notion that each unit of work has the same weight. In addition, as a direct consequence of the rounding, our algorithm also achieves a bi-criteria 2-approximation for the makespan objective. Our technical contribution is a tight analysis of the expected cost of the solution compared to the one given by the Configuration-LP relaxation - we reduce this task to that of understanding certain worst-case instances which are simple to analyze.
Starting Page	2654
Ending Page	2669
Page Count	16
File Format	PDF
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-01-16
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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