NDLI: A New Direction for Counting Perfect Matchings

Content Provider	IEEE Xplore Digital Library
Author	Izumi, T. Wadayama, T.
Copyright Year	2012
Abstract	In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq 3$, our algorithm runs with $O^{\ast}(2^{(1 - 1/O(\Delta \log \Delta))n})$ time and exponential space. Compared to the previous algorithms, it achieves a better time bound in the sense that the performance degradation to the increase of $\Delta$ is quite slower. The main idea of our algorithm is a new reduction to the problem of computing the cut-weight distribution of the input graph. The primary ingredient of this reduction is MacWilliams Identity derived from elementary coding theory. The whole of our algorithm is designed by combining that reduction with a non-trivial fast algorithm computing the cut-weight distribution. To the best of our knowledge, the approach posed in this paper is new and may be of independent interest.
Starting Page	591
Ending Page	598
File Size	278296
Page Count	8
File Format	PDF
ISBN	9781467343831
ISSN	02725428
e-ISBN	9780769548746
DOI	10.1109/FOCS.2012.28
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-10-20
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Partitioning algorithms Bipartite graph Vectors Polynomials Linear code Generators Optical wavelength conversion MacWilliams identity counting perfect matchings exponential algorithm coding theory
Content Type	Text
Resource Type	Article

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