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Optimizing busy time on parallel machines.

Mertzios, G.B. and Shalom, M. and Voloshin, A. and Wong, P.W.H. and Zaks, S. (2012) 'Optimizing busy time on parallel machines.', in Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium (IPDPS 2012). New York: IEEE, pp. 238-248.


We consider the following fundamental scheduling problem in which the input consists of n jobs to be scheduled on a set of identical machines of bounded capacity g (which is the maximal number of jobs that can be processed simultaneously by a single machine). Each job is associated with a start time and a completion time, it is supposed to be processed from the start time to the completion time (and in one of our extensions it has to be scheduled also in a continuous number of days, this corresponds to a two-dimensional version of the problem). We consider two versions of the problem. In the scheduling minimization version the goal is to minimize the total busy time of machines used to schedule all jobs. In the resource allocation maximization version the goal is to maximize the number of jobs that are scheduled for processing under a budget constraint given in terms of busy time. This is the first study of the maximization version of the problem. The minimization problem is known to be NP-Hard, thus the maximization problem is also NP-Hard. We consider various special cases, identify cases where an optimal solution can be computed in polynomial time, and mainly provide constant factor approximation algorithms for both minimization and maximization problems. Some of our results improve upon the best known results for this job scheduling problem. Our study has applications in power consumption, cloud computing and optimizing switching cost of optical networks.

Item Type:Book chapter
Keywords:Interval scheduling, Busy time, Resource allocation, Approximation algorithms
Full text:(AM) Accepted Manuscript
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Publisher statement:© 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Date accepted:No date available
Date deposited:24 April 2015
Date of first online publication:May 2012
Date first made open access:No date available

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