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Nonpreemptive scheduling of independent tasks with prespecified processor allocations
Author(s) -
Bianco L.,
Dell'Olmo P.,
Speranza M. Grazia
Publication year - 1994
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199412)41:7<959::aid-nav3220410708>3.0.co;2-k
Subject(s) - comparability , job shop scheduling , scheduling (production processes) , mathematical optimization , computer science , independent set , graph , mathematics , theoretical computer science , combinatorics , schedule , operating system
In this article we study the problem of scheduling independent tasks, each of which requires the simultaneous availability of a set of prespecified processors, with the objective of minimizing the maximum completion time. We propose a graph‐theoretical approach and identify a class of polynomial instances, corresponding to comparability graphs. We show that the scheduling problem is polynomially equivalent to the problem of extending a graph to a comparability graph whose maximum weighted clique has minimum weight. Using this formulation we show that in some cases it is possible to decompose the problem according to the canonical decomposition of the graph. Finally, a general solution procedure is given that includes a branch‐and‐bound algorithm for the solution of subproblems which can be neither decomposed nor solved in polynomial time. Some examples and computational results are presented. © 1994 John Wiley & Sons, Inc.