Replica Symmetry and Combinatorial Optimization [article]

Johan Wästlund
2009 arXiv   pre-print
We establish the soundness of the replica symmetric ansatz introduced by M. Mezard and G. Parisi for minimum matching and the traveling salesman problem in the pseudo-dimension d mean field model for d\geq 1. The case d=1 of minimum matching corresponds to the pi^2/6 limit for the assignment problem established by D. Aldous in 2001, and the analogous limit for the d=1 case of TSP was recently established by the author with a different method. We introduce a game-theoretical framework by which
more » ... prove the correctness of the replica-cavity prediction of the corresponding limits also for d>1.
arXiv:0908.1920v2 fatcat:tnaq7upd45ahzel5b3vh46fb54