Birkhoff's algorithm (also called Birkhoff-von-Neumann algorithm) is an algorithm for decomposing a bistochastic matrix into a convex combination of permutation matrices. It was published by Garrett Birkhoff in 1946.[1][2]: 36 It has many applications. One such application is for the problem of fair random assignment: given a randomized allocation of items, Birkhoff's algorithm can decompose it into a lottery on deterministic allocations.
^Birkhoff, Garrett (1946), "Tres observaciones sobre el algebra lineal [Three observations on linear algebra]", Univ. Nac. Tucumán. Revista A., 5: 147–151, MR 0020547.
^Lovász, László; Plummer, M. D. (1986), Matching Theory, Annals of Discrete Mathematics, vol. 29, North-Holland, ISBN 0-444-87916-1, MR 0859549
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Birkhoff'salgorithm (also called Birkhoff-von-Neumann algorithm) is an algorithm for decomposing a bistochastic matrix into a convex combination of permutation...
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different decompositions Birkhoffalgorithm Poincaré–Birkhoff–Witt theorem This page lists people with the surname Birkhoff. If an internal link intending...
matrices. It can be found by the Birkhoffalgorithm. This disambiguation page lists articles associated with the title Birkhoff decomposition. If an internal...
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems...
for being the first major computer-aided proof. In 1912, George David Birkhoff introduced the chromatic polynomial to study the coloring problem, which...
convex combination of permutation matrices. This can be done by the Birkhoffalgorithm. It is guaranteed to find a combination in which the number of permutation...
and Garrett Birkhoff. A Survey of Modern Algebra, Fourth Edition. MacMillan Publishing Co., 1977. ISBN 0-02-310070-2. 1–7: "The Euclidean Algorithm."...
stochastic matrix - the sum of elements in each row and each column is 1. Birkhoff'salgorithm can be used to decompose the matrix into a convex sum of at most...
Quadratic equation § Quadratic factorization Gallian 2012, p. 311 Mac Lane & Birkhoff 1999 do not explicitly define "reducible", but they use it in several places...
In the classic setting, in which m=n, this can be done using the Birkhoffalgorithm. It can decompose any n-by-n matrix of agent-object probabilities...
paper by von Neumann and Garrett Birkhoff, the first to introduce quantum logics, wherein von Neumann and Birkhoff first proved that quantum mechanics...
mathematical theory of lattices and ordered sets that was developed by Garrett Birkhoff and others in the 1930s. Formal concept analysis finds practical application...
function of the number of colors and was originally defined by George David Birkhoff to study the four color problem. It was generalised to the Tutte polynomial...
ISBN 978-3-540-57273-2 Birkhoff, Garrett (1948), Lattice Theory (Revised ed.), American Mathematical Society Chan, Hubert (2004), "A parameterized algorithm for upward...
dissection was introduced by George (1973); the name was suggested by Garrett Birkhoff. Nested dissection consists of the following steps: Form an undirected...
Huygens in his calculation of π {\displaystyle \pi } . In the words of Birkhoff and Rota, "its usefulness for practical computations can hardly be overestimated...
c. The concept of median graphs has long been studied, for instance by Birkhoff & Kiss (1947) or (more explicitly) by Avann (1961), but the first paper...
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