Abstract
In this paper we study variants of the non-preemptive parallel job scheduling problem where the number of machines is polynomially bounded in the number of jobs. For this problem we show that a schedule with length at most (1 + ε)OPT can be calculated in polynomial time, which is the best possible result (in the sense of approximation ratio), since the problem is strongly NP-hard.
For the case when all jobs must be allotted to a subset of machines with consecutive indices a schedule with length at most (1.5 + ε)OPT can be calculated in polynomial time. The previously best known results are algorithms with absolute approximation ratio 2.
Research supported by a PPP funding “Approximation algorithms for d-dimensional packing problems” 315/ab D/05/50457 granted by the DAAD, and by EU research project AEOLUS, Algorithmic Principles for Building Efficient Overlay Computers, EU contract number 015964.
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Jansen, K., Thöle, R. (2008). Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2 . In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_20
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DOI: https://doi.org/10.1007/978-3-540-70575-8_20
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