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. The key idea of the FKT algorithm is to convert the problem into a Pfaffian computation of a skew-symmetric matrix derived from a planar embedding of the graph. The Pfaffian of this matrix is then computed efficiently using standard determinant algorithms.
The Fisher–Kasteleyn–Temperley (FKT) algorithm, named after Michael Fisher, Pieter Kasteleyn, and Neville Temperley, counts the number of perfect matchings...
FKT may refer to: Falkland Islands Time Fastest known time, to complete a route FKTalgorithm, in graph theory FK Tønsberg, a Norwegian football club...
in a planar graph can be computed exactly in polynomial time via the FKTalgorithm. The number of perfect matchings in a complete graph Kn (with n even)...
the perfect matchings of the graph. This is the main idea behind the FKTalgorithm for counting perfect matchings in planar graphs, which always have Pfaffian...
is given by a Pfaffian, hence is polynomial time computable via the FKTalgorithm. This is surprising given that for general graphs, the problem is very...
H_{2}} , can be expressed as a Pfaffian and computed efficiently via the FKTalgorithm. This idea was developed by Fisher, Kasteleyn, and Temperley to compute...
matchings in a graph. For planar graphs (regardless of bipartiteness), the FKTalgorithm computes the number of perfect matchings in polynomial time by changing...
latter problem is tractable by the FKTalgorithm, which dates to the 1960s. Soon after, Valiant found holographic algorithms with reductions to matchgates...
Alma mater King's College London Known for Theory of phase transitions FKTalgorithm Awards Irving Langmuir Award (1971) Wolf Prize (1980) Boltzmann Medal...
he independently discovered combinatorial Fisher-Kasteleyn-Temperley algorithm. In a series of papers with C. M. Fortuin he developed random cluster...
of Photogrammetry, Cartography and Remote Sensing. 22: 363. Bibcode:2011ArFKT..22..363S. de Kinder, R. E. Jr.; Barnes, J. R. (August 1997). "The Generalized...
compander system - Basics and applications]. Fernseh- und Kinotechnik [de] (FKT) (Speech at the FKTG Tagung) (in German). Vol. 30, no. 12. Freiburg, Germany...
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