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 Paper Abstract and Keywords Presentation 2008-10-10 13:30 Computing the Tutte Polynomial of a Graph via BDD RevisitedHiroshi 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 Copyrightandreproduction 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 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) 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 Keyword(3) Keyword(4) Keyword(5) Keyword(6) Keyword(7) Keyword(8) 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) 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () Speaker 3 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