Approximation Schemes for the Min-Max Starting Time Problem
We consider the off-line scheduling problem of minimizing the maximal starting time. The input to this problem is a sequence of n jobs and m identical machines. The goal is to assign the jobs to the machines so that the first time in which all jobs have already started their processing is minimized, under the restriction that the processing of the jobs on any given machine must respect their original order. Our main result is a polynomial time approximation scheme for this problem in the case where m is considered as part of the input. As the input to this problem is a sequence of jobs, rather than a set of jobs where the order is insignificant, we present techniques that are designed to handle ordering constraints. Those techniques are combined with common techniques of assignment problems in order to yield a polynomial time approximation scheme.
KeywordsSchedule Problem Approximation Scheme Parallel Machine Competitive Ratio List Schedule
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- 3.Graham, R.L.: Bounds for certain multiprocessor anomalies. Bell System Technical Journal 45, 1563–1581 (1966)Google Scholar
- 8.Jansen, K., Porkolab, L.: Improved approximation schemes for scheduling unrelated parallel machines. In: Andersson, S.I. (ed.) Summer University of Southern Stockholm 1993. LNCS, vol. 888, pp. 408–417. Springer, Heidelberg (1999)Google Scholar
- 10.Mehta, S.R., Chandrasekaran, R., Emmons, H.: Order-presrving allocation of jobs to two machines. Naval Research Logistics Quarterly 21, 846–847 (1975)Google Scholar
- 11.Naor, J., Bar-Noy, A., Freund, A.: On-line load balancing in a hierarchical server topology. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 77–88. Springer, Heidelberg (1999)Google Scholar