TY - GEN

T1 - An O(log n)-competitive algorithm for online machine minimization

AU - Chen, Lin

AU - Megow, Nicole

AU - Schewior, Kevin

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2016

Y1 - 2016

N2 - We consider the online machine minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a minimum number of machines. Our main result is a general O(log m)-competitive algorithm for the online problem, where m is the optimal number of machines used in an offline solution. This is the first improvement on an intriguing problem in nearly two decades. To date, the best known result is a O(log(pmax/pmin))-competitive algorithm by Phillips et al. (STOC 1997) that depends on the ratio of maximum and minimum job sizes, pmax and pmin. Even for m = 2 no better algorithm was known. Our algorithm is in this case constant-competitive. When applied to laminar or agreeable instances, our algorithm achieves a competitive ratio of O(1) even independently of m. The following two key components lead to our new result. Firstly, we derive a new lower bound on the optimum value that relates the laxity and the number of jobs with intersecting time windows. Then, we design a new algorithm that is tailored to this lower bound and balances the delay of jobs by taking the number of currently running jobs into account.

AB - We consider the online machine minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a minimum number of machines. Our main result is a general O(log m)-competitive algorithm for the online problem, where m is the optimal number of machines used in an offline solution. This is the first improvement on an intriguing problem in nearly two decades. To date, the best known result is a O(log(pmax/pmin))-competitive algorithm by Phillips et al. (STOC 1997) that depends on the ratio of maximum and minimum job sizes, pmax and pmin. Even for m = 2 no better algorithm was known. Our algorithm is in this case constant-competitive. When applied to laminar or agreeable instances, our algorithm achieves a competitive ratio of O(1) even independently of m. The following two key components lead to our new result. Firstly, we derive a new lower bound on the optimum value that relates the laxity and the number of jobs with intersecting time windows. Then, we design a new algorithm that is tailored to this lower bound and balances the delay of jobs by taking the number of currently running jobs into account.

UR - http://www.scopus.com/inward/record.url?scp=84962920222&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84962920222

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 155

EP - 163

BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

A2 - Krauthgamer, Robert

PB - Association for Computing Machinery

Y2 - 10 January 2016 through 12 January 2016

ER -