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| In [[mathematics]], the '''computation of the [[permanent]] of a [[matrix (mathematics)|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.
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| 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 a permutation|parity of the set]], the permanent weights them all with a +1 sign.
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| While the determinant can be computed in [[polynomial time]] by [[Gaussian elimination]], the permanent cannot. In [[computational complexity theory]], [[Permanent is sharp-P-complete|a theorem of Valiant]] states that computing permanents, even of matrices in which all entries are 0 or 1, is [[sharp-P-complete|#P-complete]] {{harvtxt|Valiant|1979}} putting the computation of the permanent in a class of problems believed to be even more difficult to compute than [[NP (complexity)|NP]]. It is known that computing the permanent is impossible for logspace-uniform [[ACC0|ACC<sup>0</sup>]] circuits {{harv|Allender|Gore|1994}}.
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| 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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| ==Definition and naive algorithm==
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| The permanent of an ''n''-by-''n'' matrix ''A'' = (''a''<sub>''i,j''</sub>) is defined as
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| : <math> \operatorname{perm}(A)=\sum_{\sigma\in S_n}\prod_{i=1}^n a_{i,\sigma(i)}.</math>
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| The sum here extends over all elements σ of the [[symmetric group]] ''S''<sub>''n''</sub>, i.e. over all [[permutation]]s of the numbers 1, 2, ..., ''n''. This formula differs from the corresponding formula for the determinant only in that, in the determinant, each product is multiplied by the [[Parity of a permutation|sign of the permutation]] σ while in this formula each product is unsigned. The formula may be directly translated into an algorithm that naively expands the formula, summing over all permutations and within the sum multiplying out each matrix entry. This requires ''n!'' ''n'' arithmetic operations.
| |
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| ==Ryser formula==
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| The fastest known <ref>As of 2008, see {{harvtxt|Rempala|Wesolowski|2008}}</ref> general exact algorithm is due to [[Herbert John Ryser]] ({{harvtxt|Ryser|1963}}).
| |
| Ryser’s method is based on an [[inclusion-exclusion principle|inclusion–exclusion]] formula that can be given<ref>{{harvtxt|van Lint|Wilson|2001}} [http://books.google.com/books?id=5l5ps2JkyT0C&pg=PA108&dq=permanent+ryser&lr=#PPA99,M1 p. 99]</ref> as follows: Let <math>A_k</math> be obtained from ''A'' by deleting ''k'' columns, let <math>P(A_k)</math> be the product of the row-sums of <math>A_k</math>, and let <math>\Sigma_k</math> be the sum of the values of <math>P(A_k)</math> over all possible <math>A_k</math>. Then
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| :<math> \operatorname{perm}(A)=\sum_{k=0}^{n-1} (-1)^{k}\Sigma_k.</math>
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| It may be rewritten in terms of the matrix entries as follows<ref>{{harvtxt|CRC Concise Encyclopedia of Mathematics}}</ref>
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| : <math>\operatorname{perm} (A) = (-1)^n \sum_{S\subseteq\{1,\dots,n\}} (-1)^{|S|} \prod_{i=1}^n \sum_{j\in S} a_{ij}.</math> | |
| | |
| Ryser’s formula can be evaluated using <math>O(2^nn^2)</math> arithmetic operations, or <math>O(2^nn)</math> by processing the sets <math>S</math> in [[Gray code]] order.
| |
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| ==Glynn formula==
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| Another formula that appears to be as fast as Ryser's is closely related to the [[polarization identity]] for a [[symmetric tensor]] {{harv|Glynn|2010}}.
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| It has the formula (when the characteristic of the field is not two)
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| : <math>\operatorname{perm}(A) = \left[\sum_\delta \left(\prod_{k=1}^m \delta_k\right) \prod_{j=1}^m \sum_{i=1}^m \delta_i a_{ij}\right] / 2^{m-1},</math>
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| where the outer sum is over all <math>2^{m-1}</math> vectors <math>\delta=(\delta_1=1,\delta_2,\dots,\delta_m)\in \{\pm1\}^m</math>.
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| ==Special cases==
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| ===Planar and ''K''<sub>3,3</sub>-free===
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| The number of [[perfect matching]]s in a [[bipartite graph]] is counted by the permanent of the graph's [[biadjacency matrix]], and the permanent of any 0-1 matrix can be [[Permanent#Perfect matchings|interpreted in this way]] as the number of perfect matchings in a graph. For [[planar graph]]s (regardless of bipartiteness), the [[FKT algorithm]] computes the number of perfect matchings in polynomial time by changing the signs of a carefully chosen subset of the entries in the [[Tutte matrix]] of the graph, so that the [[Pfaffian]] of the resulting [[skew-symmetric matrix]] (the [[square root]] of its [[determinant]]) is the number of perfect matchings. This technique can be generalized to graphs that contain no subgraph [[homeomorphism (graph theory)|homeomorphic]] to the [[complete bipartite graph]] ''K''<sub>3,3</sub>.<ref>{{harvtxt|Little|1974}}, {{harvtxt|Vazirani|1988}}</ref>
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| [[George Pólya]] had asked the question<ref>{{harvtxt|Pólya|1913}}, {{harvtxt|Reich|1971}}</ref> of when it is possible to change the signs of some of the entries of a 01 matrix A so that the determinant of the new matrix is the permanent of A. Not all 01 matrices are "convertible" in this manner; in fact it is known ({{harvtxt|Marcus|Minc|1961}}) that
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| there is no linear map <math>T</math> such that <math>\operatorname{per}\,T(A) = \det A</math> for all <math>n\times n</math> matrices <math>A</math>. The characterization of "convertible" matrices was given by {{harvtxt|Little|1975}} who showed that such matrices are precisely those that are the [[biadjacency matrix]] of bipartite graphs that have a [[Pfaffian orientation]]: an orientation of the edges such that for every even cycle <math>C</math> for which <math>G\setminus C</math> has a perfect matching, there are an odd number of edges directed along C (and thus an odd number with the opposite orientation). It was also shown that these graphs are exactly those that do not contain a subgraph homeomorphic to <math>K_{3,3}</math>, as above.
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| ===Computation modulo a number=== | |
| [[modular arithmetic|Modulo]] 2, the permanent is the same as the determinant, as <math>(-1) \equiv 1 \pmod 2.</math> It can also be computed modulo <math>2^k</math> in time <math>O(n^{4k-3})</math> for <math>k \ge 2</math>. However, it is [[UP (complexity)|UP-hard]] to compute the permanent modulo any number that is not a power of 2. {{harvtxt|Valiant|1979}}
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| There are various formulae given by {{harvtxt|Glynn|2010}} for the computation modulo a prime <math>p</math>.
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| Firstly there is one using symbolic calculations with partial derivatives.
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| Secondly for <math>p=3</math> there is the following formula (Grigoriy Kogan, 1996) using the determinants of the principal
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| submatrices of the matrix:
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| :<math>\operatorname{perm} (A) = (-1)^{m}\Sigma_{U\subseteq \{1,\dots,m\}} \det(A_U).\det(A_{\bar U}),</math>
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| where <math>A_U</math> is the principal submatrix of <math>A</math> induced by the rows and columns of <math>A</math>
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| indexed by <math>U</math>, and <math>\bar U</math> is the complement of <math>U</math> in <math>\{1,\dots,m\}.</math>
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| (The determinant of an empty submatrix is defined to be 1). | |
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| This formula implies the following identities over fields of Characteristic 3 (Grigoriy Kogan, 1996):
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| for any invertible <math>A</math>
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| :<math>\operatorname{perm}(A^{-1})\det(A)^2 = \operatorname{perm}(A) </math>;
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| for any unitary <math>U</math> , i.e. a square matrix <math>U</math> such that <math>U^{T} U = I \,</math> ,
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| :<math>\operatorname{perm}(U)^2 = \det(U+V)\det(U) </math> | |
| where <math>V</math> is the matrix whose entries are the cubes of the corresponding entries of <math>U</math>.
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| ==Approximate computation==
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| When the entries of ''A'' are nonnegative, the permanent can be computed [[approximation algorithm|approximately]] in [[randomized algorithm|probabilistic]] polynomial time, up to an error of ε''M'', where ''M'' is the value of the permanent and ε > 0 is arbitrary. In other words, there exists a [[fully polynomial-time randomized approximation scheme]] (FPRAS) ({{harvtxt|Jerrum|Vigoda|Sinclair|2001}}).
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| The most difficult step in the computation is the construction of an algorithm to [[Sampling (statistics)|sample]] almost [[Uniform distribution (discrete)|uniformly]] from the set of all perfect matchings in a given bipartite graph: in other words, a fully polynomial almost uniform sampler (FPAUS). This can be done using a [[Markov chain Monte Carlo]] algorithm that uses a [[Metropolis–Hastings algorithm|Metropolis rule]] to define and run a [[Markov chain]] whose distribution is close to uniform, and whose [[Markov chain mixing time|mixing time]] is polynomial.
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| It is possible to approximately count the number of perfect matchings in a graph via the [[Random self-reducibility|self-reducibility]] of the permanent, by using the FPAUS in combination with a well-known reduction from sampling to counting due to {{harvtxt|Jerrum|Valiant|Vazirani|1986}}. Let <math>M(G)</math> denote the number of perfect matchings in <math>G</math>. Roughly, for any particular edge <math>e</math> in <math>G</math>, by sampling many matchings in <math>G</math> and counting how many of them are matchings in <math>G \setminus e</math>, one can obtain an estimate of the ratio <math>\rho=\frac{M(G)}{M(G\setminus e)}</math>. The number <math>M(G)</math> is then <math>\rho M(G \setminus e)</math>, where <math> M(G \setminus e)</math> can be approximated by applying the same method recursively.
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| ==Notes== | |
| {{reflist|colwidth=30em}}
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| ==References==
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| {{refbegin|colwidth=30em}}
| |
| *{{Citation
| |
| |last1 = Allender | first1= Eric
| |
| |last2= Gore | first2= Vivec
| |
| |title=A uniform circuit lower bound for the permanent
| |
| |journal=SIAM J. Comput. |volume=23|number=5|pages=1026–1049|year= 1994
| |
| }}
| |
| *{{citation
| |
| | author = Grigoriy Kogan
| |
| | title = Computing permanents over fields of characteristic 3: where and why it becomes difficult
| |
| | journal = 37th Annual Symposium on Foundations of Computer Science (FOCS '96)
| |
| | year = 1996
| |
| }}
| |
| | |
| *{{citation
| |
| | author = David G. Glynn
| |
| | title = The permanent of a square matrix
| |
| | journal = European Journal of Combinatorics
| |
| | volume = 31
| |
| | pages = 1887–1891
| |
| | year = 2010
| |
| | doi = 10.1016/j.ejc.2010.01.010
| |
| | issue = 7
| |
| }}
| |
| *{{Citation
| |
| |last1=Jerrum|first1=M.|last2= Sinclair|first2=A.|last3=Vigoda|first3=E.|year=2001|id={{ECCC|2000|00|079}}|contribution= A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries|title=[[Symposium on Theory of Computing|Proc. 33rd Symposium on Theory of Computing]]|pages=712–721|doi=10.1145/380752.380877
| |
| }}
| |
| *{{Citation
| |
| |author1=Mark Jerrum|author2=Leslie Valiant|author3=Vijay Vazirani|title=Random generation of combinatorial structures from a uniform distribution|journal=Theoretical Computer Science|volume=43|year=1986|pages=169–188|doi=10.1016/0304-3975(86)90174-X|authorlink1=Mark Jerrum|authorlink2=Leslie Valiant|authorlink3=Vijay Vazirani
| |
| }}
| |
| *{{Citation
| |
| | last1= van Lint | first1= Jacobus Hendricus
| |
| | last2= Wilson | first2= Richard Michale
| |
| | title= A Course in Combinatorics | year=2001
| |
| |isbn = 0-521-00601-5
| |
| }}
| |
| *{{Citation
| |
| | last = Little | first = C. H. C.
| |
| | contribution = An extension of Kasteleyn's method of enumerating the 1-factors of planar graphs
| |
| | editor-last = Holton | editor-first = D.
| |
| | pages = 63–72
| |
| | publisher = Springer-Verlag
| |
| | series = Lecture Notes in Mathematics
| |
| | title = Proc. 2nd Australian Conf. Combinatorial Mathematics
| |
| | volume = 403
| |
| | year = 1974
| |
| }}
| |
| *{{Citation
| |
| | last= Little | first= C. H. C.
| |
| | title=A characterization of convertible (0, 1)-matrices |
| |
| url= http://www.sciencedirect.com/science/article/B6WHT-4D7K7HW-H5/2/caa9448ac7c4e895fd7845515c7a68d1
| |
| |journal= J. Combin. Theory Ser. B
| |
| |volume= 18 |year=1975
| |
| | pages= 187–208
| |
| | doi= 10.1016/0095-8956(75)90048-9
| |
| | issue= 3
| |
| }}
| |
| *{{Citation
| |
| | last1=Marcus|first1= M. |last2= Minc| first2= H.
| |
| |title= On the relation between the determinant and the permanent
| |
| |journal=Illinois J. Math.
| |
| |volume= 5 |year=1961|pages= 376–381
| |
| }}
| |
| *{{Citation
| |
| |last= Pólya | first = G. |authorlink =George Pólya
| |
| |title=Aufgabe 424|journal= Arch. Math. Phys. |year= 1913| pages= 27
| |
| |volume= 20 |issue= 3
| |
| }}
| |
| *{{Citation
| |
| |last =Reich | first= Simeon
| |
| |journal= American Mathematical Monthly
| |
| |volume= 78 |year= 1971|pages=649–650
| |
| |jstor= 2316574
| |
| |title= Another solution of an old problem of pólya |issue= 6
| |
| |doi =10.2307/2316574
| |
| }}
| |
| *{{Citation
| |
| |title=Symmetric Functionals on Random Matrices and Random Matchings Problems
| |
| |first1= Grzegorz A. |last1=Rempała|first2=Jacek |last2=Wesolowski|year= 2008|isbn=0-387-75145-9|pages= 4
| |
| }}
| |
| *{{Citation
| |
| |last=Ryser| first= H. J.|authorlink=Herbert John Ryser
| |
| |title=Combinatorial Mathematics
| |
| |series=The Carus mathematical monographs
| |
| |publisher=[[The Mathematical Association of America]]
| |
| |year= 1963
| |
| }}
| |
| *{{Citation
| |
| | last = Vazirani | first = Vijay V. | author-link = Vijay Vazirani
| |
| | contribution = NC algorithms for computing the number of perfect matchings in K<sub>3,3</sub>-free graphs and related problems
| |
| | doi = 10.1007/3-540-19487-8_27
| |
| | pages = 233–242
| |
| | publisher = Springer-Verlag
| |
| | series = Lecture Notes in Computer Science
| |
| | title = Proc. 1st Scandinavian Workshop on Algorithm Theory (SWAT '88)
| |
| | volume = 318
| |
| | year = 1988
| |
| }}
| |
| *{{Citation
| |
| | author = Leslie G. Valiant
| |
| | title = The Complexity of Computing the Permanent
| |
| | journal = Theoretical Computer Science
| |
| | volume = 8
| |
| | pages = 189–201
| |
| | publisher = Elsevier
| |
| | location =
| |
| | year = 1979
| |
| | doi = 10.1016/0304-3975(79)90044-6
| |
| | issue = 2
| |
| }}
| |
| *{{Citation
| |
| | title=CRC Concise Encyclopedia of Mathematics
| |
| | contribution=Permanent
| |
| | publisher= Chapman & Hall/CRC
| |
| | year=2002
| |
| }}
| |
| {{refend}}
| |
| | |
| {{DEFAULTSORT:Computing The Permanent}}
| |
| [[Category:Computational complexity theory]]
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| [[Category:Linear algebra]]
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| [[Category:Matrix theory]]
| |
| [[Category:Permutations]]
| |
| [[Category:Computational problems]]
| |
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Electrosurgery іs useԁ in numerous medical ɑreas including dermatology, orthopedics, cardiology, ophthalmology, ɑnd аlso urology. Electrosurgery іs not brand-new, yet with the advancements mɑde in tҺіs technology, іt hɑs аctually ended up being a vital element in detailed dermatologist services. Ӎɑny physicians favor electrosurgery tօ cryosurgery оr laser device surgical treatment fоr a number of procedures. TҺe Skin Health Facility оf Alabama caters tօ the skin care demands οf thе whߋle family, consisting of children of any ages. Education is thе first step to initiate ɑ successful procedure.
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