Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2

Authors:
Klaus Jansen;Ralf Thöle
Affiliations:
Institut für Informatik, Universität zu Kiel, Germany;Institut für Informatik, Universität zu Kiel, Germany
Venue:
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Year:
2008

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Abstract

In this paper we study variants of the non-preemptive paralleljob scheduling problem where the number of machines is polynomiallybounded in the number of jobs. For this problem we show that aschedule with length at most (1 + ε)OPT can becalculated in polynomial time, which is the best possible result(in the sense of approximation ratio), since the problem isstrongly NP-hard.For the case when all jobs must be allotted to a subset ofmachines 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 absoluteapproximation ratio 2.