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Scheduling unit-length jobs with precedence constraints of small height

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Abstract

We consider the problem of scheduling unit-length jobs on identical machines subject to precedence constraints. We show that natural scheduling rules fail when the precedence constraints form a collection of stars or a collection of complete bipartite graphs. We prove that the problem is in fact NP-hard on collections of stars when the input is given in a compact encoding, whereas it can be solved in polynomial time with standard adjacency list encoding. On a subclass of collections of stars and on collections of complete bipartite graphs we show that the problem can be solved in polynomial time even when the input is given in compact encoding, in both cases via non-trivial algorithms.
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Details

Original languageEnglish
Pages (from-to)166-172
JournalOperations Research Letters
Volume42
Issue number2
DOIs
Publication statusPublished - 1 Jan 2014