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

Abstract

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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.

How to cite

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Meurdesoif, 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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  5. M.X. Goemans and D.P. Williamson, Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming. J. ACM42 (1995) 1115-1145.  Zbl0885.68088
  6. D. Karger, R. Motwani and M. Sudan, Approximate graph coloring by semidefinite programming. J. ACM45 (1998) 246-265.  Zbl0904.68116
  7. M. Krivelevich and B. Sudakov, Approximate coloring of uniform hypergraphs. DIMACS Technical Report 98-31 (1998) 15 p.  Zbl0928.05027
  8. L. Lovász, On the Shannon capacity of a graph. IEEE Trans. Inform. TheoryIT-25 (1979) 1-7.  Zbl0395.94021
  9. C. Lund and M. Yannakakis, On the hardness of approximating minimization problems. J. ACM41 (1994) 960-981.  Zbl0814.68064
  10. 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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