Paper Abstract and Keywords |
Presentation |
2011-04-22 11:25
$\pi$DDs(PiDDs): Binary Decision Diagrams for Manipulating Sets of Combinations Shin-ichi Minato (Hokkaido Univ.) COMP2011-4 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Permutations and combinations are a couple of basic concepts in elementary combinatorics. Permutations appear in various problems such as sorting, ordering, matching, coding, and many other real-life situations. In this paper, we propose a new decision diagram ``$\pi$DD,'' for compact and canonical representation of a {\em set of permutations}. $\pi$DD has efficient algebraic set operations such as union, intersection, and especially, it has a special Cartesian product operation to generate all possible composite permutations for given two sets of permutations. This is a beautiful and powerful property of $\pi$DDs.
This paper presents the data structures and the basic operation algorithms for $\pi$DDs. We also show two application examples of $\pi$DDs: designing permutation networks and analysis of Rubik's Cube. The experimental results show that $\pi$DD-based method can explore billions of permutations in a feasible time and space, using simple algebraic operations for solving the problems. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
$\pi$DD / PiDD / BDD / ZDD / Set of permutations / Combinatorial problems / / |
Reference Info. |
IEICE Tech. Rep., vol. 111, no. 20, COMP2011-4, pp. 25-32, April 2011. |
Paper # |
COMP2011-4 |
Date of Issue |
2011-04-15 (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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COMP2011-4 |
Conference Information |
Committee |
COMP |
Conference Date |
2011-04-22 - 2011-04-22 |
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(See Japanese page) |
Place (in English) |
Kyoto University |
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(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2011-04-COMP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
$\pi$DDs(PiDDs): Binary Decision Diagrams for Manipulating Sets of Combinations |
Sub Title (in English) |
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$\pi$DD |
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PiDD |
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BDD |
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ZDD |
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Set of permutations |
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Combinatorial problems |
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1st Author's Name |
Shin-ichi Minato |
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Hokkaido University (Hokkaido Univ.) |
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Speaker |
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Date Time |
2011-04-22 11:25:00 |
Presentation Time |
35 minutes |
Registration for |
COMP |
Paper # |
COMP2011-4 |
Volume (vol) |
vol.111 |
Number (no) |
no.20 |
Page |
pp.25-32 |
#Pages |
8 |
Date of Issue |
2011-04-15 (COMP) |
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