Approximation algorithms for scheduling on multiple machines
Anil Kumar, V.S.; Marathe, M.V.
Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on
Volume , Issue , 23-25 Oct. 2005 Page(s): 254 - 263
Digital Object Identifier 10.1109/SFCS.2005.21
Summary: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. We obtain 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 (3/2 and 2, respectively); (ii) better-than-two approximation guarantees for scheduling under the Lp norm for all 1 < p < ∞, improving on the 2-approximation algorithms of Azar & Epstein; and (iii) the first constant-factor multicriteria approximation algorithms that handle the weighted completion-time and any given collection of integer Lp norms. Our algorithm yields a common generalization of rounding theorems due to Karp et al and Shmoys & Tardos; among other applications, this yields an improved approximation for scheduling with resource-dependent processing times studied by Grigoriev et al.
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