Séminaire d'équipe(s) Graphs, ALgorithms and Combinatorics
Distributed Selfish Algorithms for Max-Cut game.
Lise Rodier
11 April 2014, 10:30 - 11 April 2014, 11:30 Salle/Bat : 465/PCRI-N
Contact :
Activités de recherche : Graph Theory
Résumé :
The max-cut problem is to split the set of vertices of a
graph in such a way that the sum of the weights of the edges that pass
through is maximum.
This problem can be defined as a strategic game, this problem is a
potential game and so possesses a pure Nash equilibrium which
computation is known to be PLS-complete.
We first focus on the game applied to a complete graph and, through
a potential function analysis, proved that our algorithm reaches an
equilibrium with high probability in $O(lnln{n} + ln{frac{1}
{epsilon}})$ for all $0 leq epsilon leq 1$.
For general graphs we proved that our algorithm with a fixed
probability reaches an equilibrium in $frac{|E|}{4Delta}$ expected
rounds, $Delta$ being the maximum degree of the graph and $|E|$ the
number of edges. Finally, we gave some experiments results for general
graphs.
