Document Type
Article
Publication Date
6-5-2001
Publication Title
SIAM Journal on Computing
Department
Department of Computer Science
Abstract
We consider the problem of nonpreemptive scheduling to minimize average ( weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constant-factor approximations for this problem based on solving a preemptive or linear programming relaxation and then using the solution to get an ordering on the jobs. We introduce several new techniques which generalize this basic paradigm. We use these ideas to obtain
improved approximation algorithms for one-machine scheduling to minimize average completion time with release dates. In the process, we obtain an optimal randomized on-line algorithm for the same problem that beats a lower bound for deterministic on-line algorithms. We consider extensions to the case of parallel machine scheduling, and for this we introduce two new ideas: first, we show that a preemptive one-machine relaxation is a powerful tool for designing parallel machine scheduling algorithms that simultaneously produce good approximations and have small running times; second, we show that a nongreedy “rounding” of the relaxation yields better approximations than a greedy one. We also prove a general theore mrelating the value of one- machine relaxations to that of the schedules obtained for the original m-machine problems. This theorem applies even when there are precedence constraints on the jobs. We apply this result to obtain improved approximation ratios for precedence graphs such as in-trees, out-trees, and series-parallel graphs.
DOI
10.1137/S0097539797327180
Dartmouth Digital Commons Citation
Chekuri, Chandra; Motwani, Rajeev; Natarajan, Balas; and Stein, Clifford, "Approximation Techniques for Average Completion Time Scheduling" (2001). Dartmouth Scholarship. 2064.
https://digitalcommons.dartmouth.edu/facoa/2064
