Approximately solving Maximum Clique using neural network and related heuristics

We explore neural network and related heuristic methods for the fast approximate solution of the Maximum Clique problem. One of these algorithms, Mean Field Annealing, is implemented on the Connection Machine CM-5 and a fast annealing schedule is experimentally evaluated on random graphs, as well as on several benchmark graphs. The other algorithms, which perform certain randomized local search operations, are evaluated on the same benchmark graphs, and on Sanchis graphs. One of our algorithms adjusts its internal parameters as its computation evolves. On Sanchis graphs, it nds signiicantly larger cliques than the other algorithms do. Another algorithm, GSD(;), works best overall, but is slower than the others. All our algorithms obtain signiicantly larger cliques than other simpler heuristics but run slightly slower; they obtain signiicantly smaller cliques on average than exact algorithms or more sophisticated heuristics but run considerably faster. All our algorithms are simple and inherently parallel.