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b9000A 14 approximate algorithm for P2/tree/Cmax

โœ Scribed by Giorgio Gallo; Fulvio Piccinonno

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
766 KB
Volume
72
Category
Article
ISSN
0166-218X

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โœฆ Synopsis

We consider the problem of scheduling a set of tasks whose precedence relation is representable as a directed forest, on two identical machines, in order to minimize the total completion time. A new heuristic algorithm is presented which provides a l/4 approximate solution. This algorithm is based on the idea of critical jobs, where a job is a set of tasks corresponding to a maximal tree in the forest. A critical job is one whose total duration exceeds the total duration of all other jobs. In the paper, first a l/4 approximate algorithm for the case in which no job is critical is presented, then this algorithm is extended to the general case. The l/4 approximate bound is proved to be tight. The complexity of the proposed algorithm is studied. *Research supported by "Minister0 dell'Universit8 e della Ricerca Scientifica e Tecnologica", under the National Project on "Gestione dei Russi nei sistemi flessibili di produzione".

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