# Semi-Definite positive Programming Relaxations for Graph Kn-Coloring in Frequency Assignment

Philippe Meurdesoif; Benoît Rottembourg

RAIRO - Operations Research (2010)

- Volume: 35, Issue: 2, page 211-228
- ISSN: 0399-0559

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topMeurdesoif, Philippe, and Rottembourg, Benoît. "Semi-Definite positive Programming Relaxations for Graph Kn-Coloring in Frequency Assignment." RAIRO - Operations Research 35.2 (2010): 211-228. <http://eudml.org/doc/197841>.

@article{Meurdesoif2010,

abstract = {
In this paper we will describe a new class of coloring
problems, arising from military frequency assignment, where we want to
minimize the number of distinct n-uples of colors used to color a given
set of n-complete-subgraphs of a graph.
We will propose two relaxations based on
Semi-Definite Programming models for graph and hypergraph
coloring, to approximate those (generally) NP-hard problems, as well as
a generalization of the works of Karger et al. for hypergraph coloring,
to find good feasible solutions with a probabilistic
approach.
},

author = {Meurdesoif, Philippe, Rottembourg, Benoît},

journal = {RAIRO - Operations Research},

keywords = {Discrete optimization; semidefinite programming
frequency assignment; graph coloring; hypergraph coloring.; discrete optimization; semidefinite programming; frequency assignment; hypergraph coloring},

language = {eng},

month = {3},

number = {2},

pages = {211-228},

publisher = {EDP Sciences},

title = {Semi-Definite positive Programming Relaxations for Graph Kn-Coloring in Frequency Assignment},

url = {http://eudml.org/doc/197841},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Meurdesoif, Philippe

AU - Rottembourg, Benoît

TI - Semi-Definite positive Programming Relaxations for Graph Kn-Coloring in Frequency Assignment

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 2

SP - 211

EP - 228

AB -
In this paper we will describe a new class of coloring
problems, arising from military frequency assignment, where we want to
minimize the number of distinct n-uples of colors used to color a given
set of n-complete-subgraphs of a graph.
We will propose two relaxations based on
Semi-Definite Programming models for graph and hypergraph
coloring, to approximate those (generally) NP-hard problems, as well as
a generalization of the works of Karger et al. for hypergraph coloring,
to find good feasible solutions with a probabilistic
approach.

LA - eng

KW - Discrete optimization; semidefinite programming
frequency assignment; graph coloring; hypergraph coloring.; discrete optimization; semidefinite programming; frequency assignment; hypergraph coloring

UR - http://eudml.org/doc/197841

ER -

## References

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- M. Krivelevich and B. Sudakov, Approximate coloring of uniform hypergraphs. DIMACS Technical Report 98-31 (1998) 15 p. Zbl0928.05027
- L. Lovász, On the Shannon capacity of a graph. IEEE Trans. Inform. TheoryIT-25 (1979) 1-7. Zbl0395.94021
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- S. Mahajan and H. Ramesh, Derandomizing semidefinite programming based approximation algorithms, in Proc. of the 36th Annual IEEE Symposium on Foundations of Computer Science (1995) Paper Version: 19 p. Zbl0938.68915

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