Paper Abstract and Keywords |
Presentation |
2008-10-10 13:30
Computing the Tutte Polynomial of a Graph via BDD Revisited Hiroshi Imai (Univ. Tokyo), Keiko Imai (Chuo Univ.), Yoshitake Matsumoto, Sonoko Moriyama (Univ. Tokyo) COMP2008-39 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The computation of the Tutte polynomial of a graph, even a planar one,
is \#P-complete, and yet more efficient exponential-time algorithms
have been developed. Inspired by a recent $O^*(2^n)$-time algorithm
for this problem of a graph with $n$ vertices and $m$ edges by
Bj\"{o}rklund, Husfeldt, Kaski, Koivisto, we revisit our BDD-based
algorithms devised around 1995 from the current viewpoints, where
$O^*$ ignores a polynomial factor in $m,n$. First, the problem is
shown to be solvable in $O^*(n^{n-2})$ even for graph with parallel
edges. Next, a tighter bound on the width of BDD representing all
trees of a graph is given, specificaly, using the Bell number $B_a$ of
the number of partitions of $a$-element set, $B_{n-2}$ to
$B_{n-O(n/\log n)}$. The BDD-based algorithm yet has the best time
bound for planar graphs, whose case have applications in statistical
physics, knot theory, etc., and, by the current computing power, we
demonstrate that the Tutte polynomial of a $15\times 15=225$ lattice
graph can be computed by our algorithm. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Tutte polynomial / BDD / / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 108, no. 237, COMP2008-39, pp. 41-46, Oct. 2008. |
Paper # |
COMP2008-39 |
Date of Issue |
2008-10-03 (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) |
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COMP2008-39 |
Conference Information |
Committee |
COMP |
Conference Date |
2008-10-10 - 2008-10-10 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Tohoku Univ. |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2008-10-COMP |
Language |
English (Japanese title is available) |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Computing the Tutte Polynomial of a Graph via BDD Revisited |
Sub Title (in English) |
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Keyword(1) |
Tutte polynomial |
Keyword(2) |
BDD |
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1st Author's Name |
Hiroshi Imai |
1st Author's Affiliation |
University of Tokyo (Univ. Tokyo) |
2nd Author's Name |
Keiko Imai |
2nd Author's Affiliation |
Chuo University (Chuo Univ.) |
3rd Author's Name |
Yoshitake Matsumoto |
3rd Author's Affiliation |
University of Tokyo (Univ. Tokyo) |
4th Author's Name |
Sonoko Moriyama |
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University of Tokyo (Univ. Tokyo) |
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Speaker |
Author-3 |
Date Time |
2008-10-10 13:30:00 |
Presentation Time |
30 minutes |
Registration for |
COMP |
Paper # |
COMP2008-39 |
Volume (vol) |
vol.108 |
Number (no) |
no.237 |
Page |
pp.41-46 |
#Pages |
6 |
Date of Issue |
2008-10-03 (COMP) |
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