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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
FKT_algorithm
Topics referred to by the same term
FKT may refer to: Falkland Islands Time Fastest known time, to complete a route Fin Komodo Teknologi, company of Indonesia FKT algorithm, in graph theory
FKT
Algorithm using holographic reduction
latter problem is tractable by the FKT algorithm, which dates to the 1960s. Soon after, Valiant found holographic algorithms with reductions to matchgates
Holographic_algorithm
Set of edges without common vertices
in a planar graph can be computed exactly in polynomial time via the FKT algorithm. The number of perfect matchings in a complete graph Kn (with n even)
Matching_(graph_theory)
Assigning directions to the edges of an undirected graph
planar graphs, but not for certain other graphs. They are used in the FKT algorithm for counting perfect matchings. Connex relation Diestel, Reinhard (2005)
Orientation_(graph_theory)
Problem in linear algebra
matchings in a graph. For planar graphs (regardless of bipartiteness), the FKT algorithm computes the number of perfect matchings in polynomial time by changing
Computing_the_permanent
Algebraic encoding of graph connectivity
H_{2}} , can be expressed as a Pfaffian and computed efficiently via the FKT algorithm. This idea was developed by Fisher, Kasteleyn, and Temperley to compute
Tutte_polynomial
Matching which covers every node of the graph
in a planar graph can be computed exactly in polynomial time via the FKT algorithm. The number of perfect matchings in a complete graph Kn (with n even)
Perfect_matching
the perfect matchings of the graph. This is the main idea behind the FKT algorithm for counting perfect matchings in planar graphs, which always have Pfaffian
Pfaffian_orientation
Square root of the determinant of a skew-symmetric square matrix
is given by a Pfaffian, hence is polynomial time computable via the FKT algorithm. This is surprising given that for general graphs, the problem is very
Pfaffian
Dutch physicist (1924–1996)
he independently discovered combinatorial Fisher-Kasteleyn-Temperley algorithm. In a series of papers with C. M. Fortuin he developed random cluster
Pieter_Kasteleyn
English physicist (1931–2021)
Alma mater King's College London Known for Theory of phase transitions FKT algorithm Awards Irving Langmuir Award (1971) Wolf Prize (1980) Boltzmann Medal
Michael_Fisher
generation algorithm Ant colony algorithm Breadth-first search Depth-first search Depth-limited search FKT algorithm Flood fill Graph exploration algorithm Matching
List_of_graph_theory_topics
British applied mathematician
1098/rspa.1971.0067. JSTOR 77727. S2CID 122770421. Temperley–Lieb algebra FKT algorithm "Western Gazette 7 March 2015". Archived from the original on 18 May
Neville_Temperley
of Photogrammetry, Cartography and Remote Sensing. 22: 363. Bibcode:2011ArFKT..22..363S. de Kinder, R. E. Jr.; Barnes, J. R. (August 1997). "The Generalized
Generalized_balanced_ternary
Noise reduction system
compander system - Basics and applications]. Fernseh- und Kinotechnik [de] (FKT) (Speech at the FKTG Tagung) (in German). Vol. 30, no. 12. Freiburg, Germany
High_Com
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