Weighted coloring on planar, bipartite and split graphs: Complexity and approximation
Discrete Applied Mathematics
TCP-sleek channel access scheduling for multi-hop mesh networks
Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly
Models and heuristic algorithms for a weighted vertex coloring problem
Journal of Heuristics
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Approximating the max-edge-coloring problem
Theoretical Computer Science
Improved approximation algorithms for the max-edge coloring problem
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Improved approximation algorithms for the Max Edge-Coloring problem
Information Processing Letters
Theoretical Computer Science
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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) + 驴s +w(S k ) is minimized where w(S i ) = max {w(v) :v驴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.