Elsevier

Information and Computation

Volume 195, Issues 1–2, 25 November–15 December 2004, Pages 53-65
Information and Computation

Minimizing the maximum starting time on-line

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Abstract

We study the scheduling problem of minimizing the maximum starting time on-line. The goal is to minimize the last time that a job starts. We show that while the greedy algorithm has a competitive ratio of Θ (log m), we can give a constant competitive algorithm for this problem. We also show that the greedy algorithm is optimal for resource augmentation in the sense that it requires 2m  1 machines to have a competitive ratio of 1, whereas no algorithm can achieve this with 2m  2 machines.

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A preliminary version of this paper appeared in Proceedings of the 10th European Symposium on Algorithms (ESA 2002), p. 449–460.

1

Research supported by Israel Science Foundation (Grant No. 250/01)

2

Research supported by the Netherlands Organization for Scientific Research (NWO), Project No. SION 612-061-000