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- Computing_the_permanent abstract "In mathematics, the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns. However, where the determinant weights each of these products with a ±1 sign based on the parity of the set, the permanent weights them all with a +1 sign.While the determinant can be computed in polynomial time by Gaussian elimination, the permanent cannot. In computational complexity theory, a theorem of Valiant states that computing permanents is #P-hard, and even #P-complete for matrices in which all entries are 0 or 1.Valiant (1979) This puts the computation of the permanent in a class of problems believed to be even more difficult to compute than NP. It is known that computing the permanent is impossible for logspace-uniform ACC0 circuits.(Allender & Gore 1994)The development of both exact and approximate algorithms for computing the permanent of a matrix is an active area of research.".
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- Computing_the_permanent wikiPageWikiLink ACC0.
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- Computing_the_permanent wikiPageWikiLink Designs,_Codes_and_Cryptography.
- Computing_the_permanent wikiPageWikiLink Determinant.
- Computing_the_permanent wikiPageWikiLink European_Journal_of_Combinatorics.
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- Computing_the_permanent wikiPageWikiLink Gray_code.
- Computing_the_permanent wikiPageWikiLink Homeomorphism_(graph_theory).
- Computing_the_permanent wikiPageWikiLink Inclusion–exclusion_principle.
- Computing_the_permanent wikiPageWikiLink Journal_of_Combinatorial_Theory.
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- Computing_the_permanent wikiPageWikiLink Mathematical_Association_of_America.
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- Computing_the_permanent wikiPageWikiLink Metropolis–Hastings_algorithm.
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- Computing_the_permanent wikiPageWikiLink NP_(complexity).
- Computing_the_permanent wikiPageWikiLink Parity_of_a_permutation.
- Computing_the_permanent wikiPageWikiLink Permanent.
- Computing_the_permanent wikiPageWikiLink Permutation.
- Computing_the_permanent wikiPageWikiLink Pfaffian.
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- Computing_the_permanent wikiPageWikiLink Polynomial-time_approximation_scheme.
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- Computing_the_permanent wikiPageWikiLink SWAT_and_WADS_conferences.
- Computing_the_permanent wikiPageWikiLink Sampling_(statistics).
- Computing_the_permanent wikiPageWikiLink Sharp-P-complete.
- Computing_the_permanent wikiPageWikiLink Sharp-P-completeness_of_01-permanent.
- Computing_the_permanent wikiPageWikiLink Skew-symmetric_matrix.
- Computing_the_permanent wikiPageWikiLink Square_root.
- Computing_the_permanent wikiPageWikiLink Symmetric_group.
- Computing_the_permanent wikiPageWikiLink Symmetric_tensor.
- Computing_the_permanent wikiPageWikiLink Symposium_on_Theory_of_Computing.
- Computing_the_permanent wikiPageWikiLink Theoretical_Computer_Science_(journal).
- Computing_the_permanent wikiPageWikiLink Time_complexity.
- Computing_the_permanent wikiPageWikiLink Tutte_matrix.
- Computing_the_permanent wikiPageWikiLink UP_(complexity).
- Computing_the_permanent wikiPageWikiLink Uniform_distribution_(discrete).
- Computing_the_permanent wikiPageWikiLinkText "Computing the permanent".
- Computing_the_permanent wikiPageWikiLinkText "Computing the permanent#Ryser formula".
- Computing_the_permanent wikiPageWikiLinkText "Ryser formula".
- Computing_the_permanent wikiPageWikiLinkText "approximating the permanent".
- Computing_the_permanent wikiPageWikiLinkText "computing the permanent".
- Computing_the_permanent authorlink "H. J. Ryser".
- Computing_the_permanent first "H. J.".
- Computing_the_permanent last "Ryser".
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- Computing_the_permanent year "1963".
- Computing_the_permanent subject Category:Computational_complexity_theory.
- Computing_the_permanent subject Category:Computational_problems.
- Computing_the_permanent subject Category:Linear_algebra.
- Computing_the_permanent subject Category:Matrix_theory.
- Computing_the_permanent subject Category:Permutations.
- Computing_the_permanent hypernym Problem.
- Computing_the_permanent type Disease.
- Computing_the_permanent type Combinatoric.
- Computing_the_permanent type Function.
- Computing_the_permanent type Redirect.
- Computing_the_permanent comment "In mathematics, the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns.".
- Computing_the_permanent label "Computing the permanent".
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