Affiliation:
1. Virginia Tech., Blacksburg, Virginia
2. IBM T. J. Watson Research Center, Hawthorne, New York
3. University of Maryland, College Park, Maryland
Abstract
We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming-, quadratic programming-, and convex programming-relaxations for scheduling to minimize completion time, makespan, and other well-studied objective functions. This algorithm leads to the following applications for the general setting of unrelated parallel machines: (i) a bicriteria algorithm for a schedule whose weighted completion-time and makespan
simultaneously
exhibit the current-best individual approximations for these criteria; (ii) better-than-two approximation guarantees for scheduling to minimize the
L
p
norm of the vector of machine-loads, for all 1 <
p
< ∞; and (iii) the first constant-factor multicriteria approximation algorithms that can handle the weighted completion-time and
any
given collection of integer
L
p
norms. Our algorithm has a natural interpretation as a melding of linear-algebraic and probabilistic approaches. Via this view, it yields a common generalization of rounding theorems due to Karp et al. [1987] and Shmoys & Tardos [1993], and leads to improved approximation algorithms for the problem of scheduling with resource-dependent processing times introduced by Grigoriev et al. [2007].
Funder
Centers for Disease Control and Prevention
National Science Foundation
National Institute of General Medical Sciences
Defense Threat Reduction Agency
Division of Computer and Network Systems
Division of Social and Economic Sciences
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
33 articles.
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