NDLI: Generalized machine activation problems

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Optimal bounds for Johnson-Lindenstrauss transforms and streaming problems with sub-constant error

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Generalized machine activation problems

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Generalized machine activation problems

Content Provider	ACM Digital Library
Author	Li, Jian Khuller, Samir
Abstract	In this paper we consider a generalization of the machine activation problem introduced recently ["Energy efficient scheduling via partial shutdown" by Khuller, Li and Saha (ACM-SIAM 2010 Symp. on Discrete Algorithms)] where the unrelated parallel machine scheduling problem is studied with machine activation cost. This is the standard unrelated parallel machine scheduling problem with a machine dependent activation cost that is incurred, if any job is assigned to the machine. The problem asks for a choice of machines to activate, and a schedule of all jobs on the active machines subject to the makespan constraint. The goal is to minimize the total activation cost. Our main generalization consists of a general activation cost model, where the activation cost for a machine is a non-decreasing function of its load. We develop a greedy algorithm that yields a fractional assignment of jobs, such that at least n ™ ε jobs are assigned fractionally and the total cost is at most 1 + ln(n/ε) times the optimum. Combining with standard rounding methods yields improved bounds for several machine activation problems. In addition, we study the machine activation problem with d linear constraints (these could model makespan constraints, as well as other types of constraints). Our method yields a schedule with machine activation cost of O(1/ε log n) times the optimum and a constraint violation by a factor of 2d + ε. This result matches our previous bound for the case d = 1. As a by-product, our method also yields a ln n + 1 approximation factor for the non-metric universal facility location problem for which the cost of opening a facility is an arbitrary non-decreasing function of the number of clients assigned to it. This gives an affirmative answer to the open question posed in earlier work on universal facility location.
Starting Page	80
Ending Page	94
Page Count	15
File Format	PDF
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-01-23
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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