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Time slot scheduling of compatible jobs

Demange, Marc; de Werra, Dominique; Monnot, Jérôme; Paschos, Vangelis (2007), Time slot scheduling of compatible jobs, Journal of Scheduling, 10, 2, p. 111-127. http://dx.doi.org/10.1007/s10951-006-0003-7

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Type
Article accepté pour publication ou publié
Date
2007
Journal name
Journal of Scheduling
Volume
10
Number
2
Publisher
Springer
Pages
111-127
Publication identifier
http://dx.doi.org/10.1007/s10951-006-0003-7
Metadata
Show full item record
Author(s)
Demange, Marc
de Werra, Dominique
Monnot, Jérôme cc
Paschos, Vangelis
Abstract (EN)
A version of weighted coloring of a graph is introduced which is motivated by some types of scheduling problems: each node v of a graph G corresponds to some operation to be processed (with a processing time w(v)), edges represent nonsimultaneity requirements (incompatibilities). We have to assign each operation to one time slot in such a way that in each time slot, all operations assigned to this slot are compatible; the length of a time slot will be the maximum of the processing times of its operations. The number k of time slots to be used has to be determined as well. So, we have to find a k-coloring $${\cal S}$$= $$({S_{1},\ldots ,S_{k}})$$ of G such that w(S 1) + ⋅s +w(S k ) is minimized where w(S i ) = max {w(v) :v∊V}. Properties of optimal solutions are discussed, and complexity and approximability results are presented. Heuristic methods are given for establishing some of these results. The associated decision problems are shown to be NP-complete for bipartite graphs, for line-graphs of bipartite graphs, and for split graphs.
Subjects / Keywords
Batch scheduling; Edge coloring; Approximations; Chromatic scheduling; Weighted coloring

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