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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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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)  
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)  
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  
4th Author's Affiliation University of Tokyo (Univ. Tokyo)
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Speaker
Date Time 2008-10-10 13:30:00 
Presentation Time 30 
Registration for COMP 
Paper # IEICE-COMP2008-39 
Volume (vol) IEICE-108 
Number (no) no.237 
Page pp.41-46 
#Pages IEICE-6 
Date of Issue IEICE-COMP-2008-10-03 


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