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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
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 2011-04-22 - 2011-04-22 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyoto University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
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)  
Keyword(1) $\pi$DD  
Keyword(2) PiDD  
Keyword(3) BDD  
Keyword(4) ZDD  
Keyword(5) Set of permutations  
Keyword(6) Combinatorial problems  
1st Author's Name Shin-ichi Minato  
1st Author's Affiliation Hokkaido University (Hokkaido Univ.)
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Date Time 2011-04-22 11:25:00 
Presentation Time 35 
Registration for COMP 
Paper # IEICE-COMP2011-4 
Volume (vol) IEICE-111 
Number (no) no.20 
Page pp.25-32 
#Pages IEICE-8 
Date of Issue IEICE-COMP-2011-04-15 

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