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Paper Abstract and Keywords
Presentation 2012-09-03 16:10
A New Direction for Counting Perfect Matchings
Taisuke Izumi, Tadashi Wadayama (Nagoya Inst. of Tech.) COMP2012-33
Abstract (in Japanese) (See Japanese page) 
(in English) 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. The
full version of this paper will be presented and published at the
53rd Annual IEEE Symposium on Foundataions of Computer Science.
Keyword (in Japanese) (See Japanese page) 
(in English) counting perfect matchings / exponential algorithm / coding theory / MacWilliams identity / / / /  
Reference Info. IEICE Tech. Rep., vol. 112, no. 199, COMP2012-33, pp. 49-49, Sept. 2012.
Paper # COMP2012-33 
Date of Issue 2012-08-27 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF COMP2012-33

Conference Information
Committee COMP  
Conference Date 2012-09-03 - 2012-09-03 
Place (in Japanese) (See Japanese page) 
Place (in English) Hosei University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2012-09-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A New Direction for Counting Perfect Matchings 
Sub Title (in English)  
Keyword(1) counting perfect matchings  
Keyword(2) exponential algorithm  
Keyword(3) coding theory  
Keyword(4) MacWilliams identity  
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Keyword(6)  
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1st Author's Name Taisuke Izumi  
1st Author's Affiliation Nagoya Institute of Technology (Nagoya Inst. of Tech.)
2nd Author's Name Tadashi Wadayama  
2nd Author's Affiliation Nagoya Institute of Technology (Nagoya Inst. of Tech.)
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Speaker Author-1 
Date Time 2012-09-03 16:10:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2012-33 
Volume (vol) vol.112 
Number (no) no.199 
Page p.49 
#Pages 1 
Date of Issue 2012-08-27 (COMP) 

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