DMCA
APPROXIMATION ALGORITHMS FOR SCHEDULING UNRELATED PARALLEL MACHINES (1990)
| Citations: | 266 - 7 self |
BibTeX
@MISC{Lenstra90approximationalgorithms,
author = {Jan Karel Lenstra and David B. Shmoys and Éva Tardos},
title = { APPROXIMATION ALGORITHMS FOR SCHEDULING UNRELATED PARALLEL MACHINES},
year = {1990}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We consider the following scheduling problem. There are m parallel machines and n independent.jobs. Each job is to be assigned to one of the machines. The processing of.job j on machine i requires time Pip The objective is to lind a schedule that minimizes the makespan. Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints. In contrast to our main result, we prove that no polynomial algorithm can achieve a worst-case ratio less than ~ unless P = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.
Keyphrases
polynomial algorithm main result parallel machine fractional extreme point polynomial method fixed number approximation result scheduling problem worst-case ratio integral point linear program polynomial approximation scheme linear programming relaxation complexity classification special case time pip
