TY - JOUR

T1 - New algorithms for an ancient scheduling problem

AU - Bartal, Yair

AU - Fiat, Amos

AU - Karloff, Howard

AU - Vohra, Rakesh

PY - 1995/12

Y1 - 1995/12

N2 - We consider the on-line version of the original m-machine scheduling problem: given m machines and n positive real jobs, schedule the n jobs on the m machines so as to minimize the makespan, the completion time of the last job. In the on-line version, as soon as job j arrives, it must be assigned immediately to one of the m machines. We present two main results. The first is a (2 - ε)-competitive deterministic algorithm for all m. The competitive ratio of all previous algorithms approaches 2 as m → ∞. Indeed, the problem of improving the competitive ratio for large m had been open since 1966, when the first algorithm for this problem appeared. The second result is an optimal randomized algorithm for the case m = 2. To the best of our knowledge, our 4/3-competitive algorithm is the first specifically randomized algorithm for the original, m-machine, on-line scheduling problem.

AB - We consider the on-line version of the original m-machine scheduling problem: given m machines and n positive real jobs, schedule the n jobs on the m machines so as to minimize the makespan, the completion time of the last job. In the on-line version, as soon as job j arrives, it must be assigned immediately to one of the m machines. We present two main results. The first is a (2 - ε)-competitive deterministic algorithm for all m. The competitive ratio of all previous algorithms approaches 2 as m → ∞. Indeed, the problem of improving the competitive ratio for large m had been open since 1966, when the first algorithm for this problem appeared. The second result is an optimal randomized algorithm for the case m = 2. To the best of our knowledge, our 4/3-competitive algorithm is the first specifically randomized algorithm for the original, m-machine, on-line scheduling problem.

UR - http://www.scopus.com/inward/record.url?scp=0029531044&partnerID=8YFLogxK

U2 - 10.1006/jcss.1995.1074

DO - 10.1006/jcss.1995.1074

M3 - Article

AN - SCOPUS:0029531044

SN - 0022-0000

VL - 51

SP - 359

EP - 366

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 3

ER -