Optimization by reduction to maximum clique

MAX-CLIQUE is the optimization problem of finding a largest clique in a given graph. By reduction to MAX-CLIQUE, the following three NP-hard optimization problems in a binary weights Hopfield net special case are solved: minimum vertex and set cover, constraint satisfaction problems (N-queens), and Boolean satisfiability (using a recent reduction). The approximation performance is experimentally determined on uniformly-at-random generated instances. The author´s optimizing dynamics are discrete and converge, independently of the problem, in O(number of units) unit-switches. Several problems are optimized in a single binary weights (0/-1) network, which, for all problems, admits no invalid solutions. All reductions, except one, are goodness-preserving in a formal sense. This is contrasted with the variety of handcrafted energy functions for the same individual problems in the literature, several of which admit invalid solutions