Scheduling UET task systems with concurrency on two parallel identical processors

Problems with unit execution time tasks and two identical parallel processors have received a great deal of attention in scheduling theory. In contrast to the conventional models, where each task requires only one processor, we consider a situation when a task may require both processors simultaneously. For problems without precedence constraints we present several polynomial time algorithms which complement recent results of Lee and Cai. We also show that the introduction of precedence constraints leads to NP-hardness results for maximum lateness and mean flow time objective functions. For the maximum lateness problem, a family of algorithms, based upon the idea of modified due dates, is considered. The worst case behaviour of these algorithms is analysed, and it is shown that the same upper bound is tight for each algorithm of this family.

Authors and Affiliations

1. Universität Osnabrück, Fachbereich Mathematik/Informatik, D-49069 Osnabrück, Germany, , , , , , DE

   Peter Brucker & Sigrid Knust

2. University of Western Sydney, Nepean, Department of Mathematics, PO Box 10, Kingswood, NSW 2747, Australia, , , , , , AU

   Duncan Roper

3. University of Technology, Sydney, School of Mathematical Sciences, PO Box 123, Broadway, NSW 2007, Australia, , , , , , AU

   Yakov Zinder

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