FKT algorithm

Algorithm for counting perfect matchings in planar graphs

The Fisher–Kasteleyn–Temperley (FKT) algorithm, named after Michael Fisher, Pieter Kasteleyn, and Neville Temperley, counts the number of perfect matchings in a planar graph in polynomial time. This same task is #P-complete for general graphs. For matchings that are not required to be perfect, counting them remains #P-complete even for planar graphs.

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