%0 Journal Article
%J J. ACM
%D 2009
%T A unified approach to scheduling on unrelated parallel machines
%A Kumar,V. S. Anil
%A Marathe,Madhav V.
%A Parthasarathy,Srinivasan
%A Srinivasan, Aravind
%K Approximation algorithms
%K Randomized rounding
%K scheduling under multiple criteria
%X 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 Lp 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 Lp 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].
%B J. ACM
%V 56
%P 28:1–28:31 - 28:1–28:31
%8 2009/08//
%@ 0004-5411
%G eng
%U http://doi.acm.org/10.1145/1552285.1552289
%N 5
%R 10.1145/1552285.1552289