A Discrete Neural Algorithm for the Maximum CliqueProblem : Analysis and Circuit Implementation

For the Maximum Clique problem we propose a neural approximation algorithm that can be implemented on Field Programmable Gate Arrays (FPGA). The algorithm builds a sequence of discrete Hoppeld networks that, in polynomial time, converge to a state representing a clique for a given graph. Some experiments made on the DIMACS benchmark show that the approximated solutions found are satisfactory. Moreover the simplicity of the algorithm makes it easy to design a uniform family of circuits of small size (10n 2 log n).