Application of statistical mechanics to NP-complete problems in combinatorial optimisation
Y Fu, Philip Warren Anderson · Journal of Physics A Mathematical and General · 1986
Recently developed techniques of the statistical mechanics of random systems are applied to the graph partitioning problem. The averaged cost function is calculated and agrees well with numerical results. The problem bears close resemblance to that of spin glasses. The authors find a spin glass transition in the system, and the low temperature phase space has an ultrametric structure. This sheds light on the nature of hard computation problems.