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The Computer Journal 2001 44(3):163-173; doi:10.1093/comjnl/44.3.163
© 2001 by British Computer Society
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Precedence Constrained Scheduling: A Case in P

Kostas Politopoulos1, George F. Georgakopoulos2 and Panagiotis Tsanakas1

1 National Technical University of Athens, Department of Electrical & Computer Engineering, Athens, Greece Email: poli@cslab.ece.ntua.gr 2 University of Crete, Computer Science Department, Heraklion, Crete, Greece

‘Unit execution time’ precedence constrained scheduling (UET) is an NP-complete problem with very few special cases known to be solvable in P-time. In this article we present a practically useful case of UET solvable in P-time: we show that if the task graph is given in levels that are ‘locally’ of in-degree two and of ‘width’ more than 1.55 times the number of processors (plus 1), then an optimal schedule can be found in P-time. Task graphs which represent algebraic computations fall ordinarily in this category. Our algorithm is based on a limited look-ahead technique which allows us to use it in an on-line fashion. In the appendix we give two short NP-completeness proofs which suggest that both ‘width’ and ‘degree’ restrictions are needed to get a polynomially solvable subcase.

Received 25 February, 1999. Revised 14 March, 2001.


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