We suggest a new optical solution for solving the YES NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then to pick the correct one. In our case the device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible covers (exact or not) of the given set. For selecting the correct solution we assign to each item, from the set to be covered, a special integer number. These numbers will actually represent delays induced to light when it passes through arcs. The solution is represented as a subray arriving at a certain moment in the destination node. This will tell us if an exact cover does exist or not.
An optical system which finds solutions to the 6-city TSP using a Kohonen-type network was proposed in @cite_7 . The system shows robustness with regard to the light intensity fluctuations and weight discretization which have been simulated. Using these heuristic methods, a relatively large number of TSP cities can be handled.
@cite_7
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A systems is described which finds solutions to the 6-city TSP using a Kohonen-type network. The system shows robustness with regard to the light intensity fluctuations and weight discretization which have been simulated. Scalability to larger size problems appears straightforward.