Approximating the Permanent
نویسندگان
چکیده
منابع مشابه
Approximating the Permanent
A randomised approximation scheme for the permanent of a 0-1 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 graph. For a wide class of 0-1 matrices the approximation scheme is fully-polynomial, i.e., runs in time p...
متن کاملApproximating the α - permanent
The standard matrix permanent is the solution to a number of combinatorial and graph-theoretic problems, and theα-weighted permanent is the density function for a class of Cox processes called boson processes. The exact computation of the ordinary permanent is known to be #P-complete, and the same appears to be the case for the α-permanent for most values of α. At present, the lack of a satisfa...
متن کاملApproximating the permanent with fractional belief propagation
We discuss schemes for exact and approximate computations of permanents, and compare them with each other. Specifically, we analyze the belief propagation (BP) approach and its fractional belief propagation (FBP) generalization for computing the permanent of a non-negative matrix. Known bounds and Conjectures are verified in experiments, and some new theoretical relations, bounds and Conjecture...
متن کاملApproximating the Permanent via Nonabelian Determinants
Since the celebrated work of Jerrum, Sinclair, and Vigoda, we have known that the permanent of a {0, 1} matrix can be approximated in randomized polynomial time by using a rapidly mixing Markov chain to sample perfect matchings of a bipartite graph. A separate strand of the literature has pursued the possibility of an alternate, algebraic polynomial-time approximation scheme. These schemes work...
متن کاملApproximating the Permanent with Belief Propagation
This work describes a method of approximating matrix permanents efficiently using belief propagation. We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this partition function. After deriving some speedups to standard belief propagation, the resulting algorithm requires O(n) time per iteration and seems empirical...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1989
ISSN: 0097-5397,1095-7111
DOI: 10.1137/0218077