Approximately Counting Perfect and General Matchings in Bipartite and General Graphs
نویسنده
چکیده
Approximately Counting Perfect And General Matchings in Bipartite and General Graphs
منابع مشابه
On Counting Perfect Matchings in General Graphs
Counting perfect matchings has played a central role in the theory of counting problems. The permanent, corresponding to bipartite graphs, was shown to be #P-complete to compute exactly by Valiant (1979), and a fully polynomial randomized approximation scheme (FPRAS) was presented by Jerrum, Sinclair, and Vigoda (2004) using a Markov chain Monte Carlo (MCMC) approach. However, it has remained a...
متن کاملMatchings in Graphs
We know that counting perfect matchings is polynomial time when we restrict ourselves to the class of planar graphs. Generally speaking, the decision and search versions of a problem turn out to be “easier” than the counting question. For example, the problem of determining if a perfect matching exists, and finding one when it does, is polynomial time in general graphs, while the question of co...
متن کاملThe Polynomially Bounded Perfect Matching Problem Is in NC 2
The perfect matching problem is known to be in ¶, in randomized NC, and it is hard for NL. Whether the perfect matching problem is in NC is one of the most prominent open questions in complexity theory regarding parallel computations. Grigoriev and Karpinski [GK87] studied the perfect matching problem for bipartite graphs with polynomially bounded permanent. They showed that for such bipartite ...
متن کاملCounting the Number of Matchings in Chordal and Chordal Bipartite Graph Classes
We provide polynomial-time algorithms for counting the number of perfect matchings and the number of matchings in chain graphs, cochain graphs, and threshold graphs. These algorithms are based on newly developed subdivision schemes that we call a recursive decomposition. On the other hand, we show the #P-completeness for counting the number of perfect matchings in chordal graphs, split graphs a...
متن کاملThe algebra of set functions II: An enumerative analogue of Hall's theorem for bipartite graphs
Triesch (1997) [25] conjectured that Hall's classical theorem on matchings in bipartite graphs is a special case of a phenomenon of monotonicity for the number of matchings in such graphs. We prove this conjecture for all graphs with sufficiently many edges by deriving an explicit monotonic formula counting matchings in bipartite graphs. This formula follows from a general duality theory which ...
متن کامل