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Exponential time complexity of the permanent and the Tutte polynomial
 in Proceedings of the 37th International Colloquium on Automata, Languages and Programming, ICALP 2010, ser. Lecture Notes in Computer Science
, 2010
"... We show conditional lower bounds for wellstudied #Phard problems: ◦ The number of satisfying assignments of a 2CNF formula with n variables cannot be computed in time exp(o(n)), and the same is true for computing the number of all independent sets in an nvertex graph. ◦ The permanent of an n × n ..."
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Cited by 10 (4 self)
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× n matrix with entries 0 and 1 cannot be computed in time exp(o(n)). ◦ The Tutte polynomial of an nvertex multigraph cannot be computed in time exp(o(n)) at most evaluation points (x, y) in the case of multigraphs, and it cannot be computed in time exp(o(n / poly log n)) in the case of simple graphs
Approximating the permanent
 SIAM J. Computing
, 1989
"... Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the ..."
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Cited by 345 (26 self)
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in the graph. For a wide class of 01 matrices the approximation scheme is fullypolynomial, i.e., runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output. This class includes all dense matrices (those that contain sufficiently many l’s) and almost all sparse
Polynomial Time Algorithms To Approximate Permanents And Mixed Discriminants Within A Simply Exponential Factor
 Random Structures & Algorithms
, 1999
"... We present real, complex, and quaternionic versions of a simple randomized polynomial time algorithm to approximate the permanent of a nonnegative matrix and, more generally, the mixed discriminant of positive semidefinite matrices. The algorithm provides an unbiased estimator, which, with high pro ..."
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Cited by 39 (5 self)
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We present real, complex, and quaternionic versions of a simple randomized polynomial time algorithm to approximate the permanent of a nonnegative matrix and, more generally, the mixed discriminant of positive semidefinite matrices. The algorithm provides an unbiased estimator, which, with high
Complexity of the cover polynomial
, 2007
"... The cover polynomial introduced by Chung and Graham is a twovariate graph polynomial for directed graphs. It counts the (weighted) number of ways to cover a graph with disjoint directed cycles and paths, it is an interpolation between determinant and permanent, and it is believed to be a directed an ..."
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Cited by 11 (3 self)
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polynomial is #Phard under polynomialtime Turing reductions, while only three points are easy. Our construction uses a gadget which is easier to analyze and more general than the XORgadget used by Valiant in his proof that the permanent is #Pcomplete.
PolynomialTime Approximation of the Permanent *
"... Abstract Despite its apparent similarity to the (easilycomputable) determinant, it is believed that there is no polynomialtime algorithm for computing the permanent of an arbitrary matrix. In this survey, we review the known approaches for efficiently estimating the permanent and discuss their re ..."
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Abstract Despite its apparent similarity to the (easilycomputable) determinant, it is believed that there is no polynomialtime algorithm for computing the permanent of an arbitrary matrix. In this survey, we review the known approaches for efficiently estimating the permanent and discuss
A simple polynomial time algorithm to approximate the permanent within a simply exponential factor
 MSRI
, 1998
"... Abstract. We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of n positive semidefinite n×n matrices within a factor 2 O(n). Consequently, the algorithm allows us to approximate in randomized polynomial time the permanent of a given n×n nonnegative matrix ..."
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Cited by 5 (1 self)
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Abstract. We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of n positive semidefinite n×n matrices within a factor 2 O(n). Consequently, the algorithm allows us to approximate in randomized polynomial time the permanent of a given n×n non
Clifford Algebras and approximating the permanent
, 2002
"... We study approximation algorithms for the permanent of an n * n (0, 1) matrix A based on the following simple idea: obtain a random matrix B by replacing each 1entry of A independently by+e, where e is a random basis element of a suitable algebra; then output  det(B)2. This estimator is always ..."
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Cited by 20 (2 self)
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unbiased, but it may have exponentially large variance. In our first main result we show that, if we take the algebra to be a Clifford algebra of dimension polynomial in n, then we get an estimator with small variance. Hence only a constant number of trials suffices to estimate the permanent to good
Deterministic polynomial identity testing in non commutative models
 Computational Complexity
, 2004
"... We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: 1. Non Commutative Arithmetic Formulas: The algorithm gets as an input an arithmetic formula in the noncommuting variables x1,..., xn and determines whether or not the output of the formula ..."
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Cited by 54 (10 self)
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expression). One application is a deterministic polynomial time identity testing for setmultilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for noncommutative algebraic branching programs as defined by Nisan. Finally, we observe an exponential
Permanent Member
, 2006
"... Twoplayer completeinformation game trees are perhaps the simplest possible setting for studying generalsum games and the computational problem of finding equilibria. These games admit a simple bottomup algorithm for finding subgame perfect Nash equilibria efficiently. However, such an algorithm ..."
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can fail to identify optimal equilibria, such as those that maximize social welfare. The reason is that, counterintuitively, probabilistic action choices are sometimes needed to achieve maximum payoffs. We provide a novel polynomialtime algorithm for this problem that explicitly reasons about
Approximating the Permanent of Graphs with Large Factors
 Proceedings of the 29th IEEE Symposium on Foundations of Computer Science
, 1992
"... Let G = (U; V; E) be a bipartite graph with jU j = jV j = n. The factor size of G, f , is the maximum number of edge disjoint perfect matchings in G. We characterize the complexity of counting the number of perfect matchings in classes of graphs parameterized by factor size. We describe the simple ..."
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Cited by 29 (2 self)
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algorithm, which is an approximation algorithm for the permanent that is a natural simplification of the algorithm suggested in [Broder 86] and analyzed in [Jerrum, Sinclair 88a, 88b]. Compared to the algorithm in [Jerrum, Sinclair 88a, 88b], the simple algorithm achieves a polynomial speed up
Results 1  10
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66