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| Presentation | 2011-12-16 10:00 Relationship Between Coding Theory and Counting Perfect Matchings Taisuke Izumi, Tadashi Wadayama (NITech)  COMP2011-37 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Counting perfect matchings is known as one of the hard problems to obtain exact results, which is proven to be \#P-complete even if we restrict input graphs to 3-regular bipartite ones. In this paper, we show a polynomial-space $\tilde{O}(2^{5n/12})$-time algorithm to compute the exact number of perfect matchings for any 3-regular bipartite graph. This algorithm is derived from the coding-theoretic perspective of the cut and circuit spaces of the input graph. We can interpret their relationship to the duality of linear codes associated with two spaces, which yields the reduction of counting perfect matchings to the computation of cut-space weight distribution. Our algoirthm is obtained by designing a faster algorithm for calculating that distribution. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | counting perfect matchings / exponential algorithm / coding theory / linear code / MacWilliams identity / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 111, no. 360, COMP2011-37, pp. 9-15, Dec. 2011. | |
| Paper # | COMP2011-37 | |
| Date of Issue | 2011-12-09 (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 | COMP2011-37 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2011-12-16 - 2011-12-16 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Nagoya Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2011-12-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Relationship Between Coding Theory and Counting Perfect Matchings |
| Sub Title (in English) | |
| Keyword(1) | counting perfect matchings |
| Keyword(2) | exponential algorithm |
| Keyword(3) | coding theory |
| Keyword(4) | linear code |
| Keyword(5) | MacWilliams identity |
| Keyword(6) | |
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| Keyword(8) | |
| 1st Author's Name | Taisuke Izumi |
| 1st Author's Affiliation | Nagoya Institute of Technology (NITech) |
| 2nd Author's Name | Tadashi Wadayama |
| 2nd Author's Affiliation | Nagoya Institute of Technology (NITech) |
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| Speaker | Author-1 |
| Date Time | 2011-12-16 10:00:00 |
| Presentation Time | 30 minutes |
| Registration for | COMP |
| Paper # | COMP2011-37 |
| Volume (vol) | vol.111 |
| Number (no) | no.360 |
| Page | pp.9-15 |
| #Pages | 7 |
| Date of Issue | 2011-12-09 (COMP) |
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