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

  title={Semi-Definite positive Programming Relaxations for Graph Kn-Coloring in Frequency Assignment},
  author={Philippe Meurdesoif and Beno{\^i}t Rottembourg},
  journal={RAIRO Oper. Res.},
Dans cet article, nous decrivons une nouvelle classe de problemes de coloration rencontres en Allocation de Frequences militaire: nous voulons minimiser le nombre de n-uplets distincts utilises pour colorier un ensemble done de n-cliques d'un graphe. Pour approcher ces problemes generalement NP-difficiles, nous proposons deux relaxations basees sur les modelisations semi-definies de la coloration de graphes et d'hypergraphes, ainsi qu'une generalisation des travaux de Karger et al. a la… 
1 Citations

Figures from this paper

The dynamics of proving uncolourability of large random graphs: I. Symmetric colouring heuristic
We study the dynamics of a backtracking procedure capable of proving uncolourability of graphs, and calculate its average running time T for sparse random graphs, as a function of the average degree


Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION
Polynomial-time approximation algorithms with non-trivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph into k blocks so as to maximise
On the hardness of approximating minimization problems
It is proved that there is an c >0 such that Graph Coloring cannot be approximated with ratio n’ unless P=NP unless NP is contained in DTIME[nPOIY log ~ ].
Approximate coloring of uniform hypergraphs
Approximate graph coloring by semidefinite programming
A duality relationship established between the value of the optimum solution to the authors' semidefinite program and the Lovász &thgr;-function is established and lower bounds on the gap between the best known approximation ratio in terms of n are shown.
Derandomizing semidefinite programming based approximation algorithms
  • S. Mahajan, R. Hariharan
  • Computer Science, Mathematics
    Proceedings of IEEE 36th Annual Foundations of Computer Science
  • 1995
This paper gives techniques to derandomize the above class of randomized algorithms, thus obtaining polynomial time deterministic algorithms with the same approximation ratios for the above problems.
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.
On the Shannon capacity of a graph
  • L. Lovász
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 1979
It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases.
Sdppack User's Guide
SDPpack is a package of Matlab les designed to solve semideenite programs (SDP) and provides certain specialized routines, one to solve SDP's with only diagonal constraints, and one to compute the Lovv asz function of a graph, using the XZ search direction.
Optimisation stochastique et allocation de plans de fréquences pour des réseaux à évasion de fréquences
  • Thèse de doctorat, Université de Rennes 1
  • 1996