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Paper Abstract and Keywords
Presentation 2011-09-06 15:20
Visualization of the Phase Transition Phenomena on K-satisfiability Problem through Principal Component Analysis
Yasuaki Akazawa (Waseda Univ.), Masato Okada (Univ. Tokyo), Masato Inoue (Waseda Univ.) PRMU2011-78 IBISML2011-37
Abstract (in Japanese) (See Japanese page) 
(in English) In this manuscript, we study about the random K-satisfiability (K-SAT) problem through numerical simulation. K-SAT problem is the standard problem of an NP-complete problem, but its phase transition phenomena are still in question. It has been only partially solved by analytical methods when the system size (the number of dimensions of boolean variables) is infinity. Through Markov chain Monte Carlo (MCMC) simulation, we show intuitive two-dimensional histograms of empirical distributions of the system and eigenvalue distributions by using the principal component analysis (PCA). We also show histograms of spin-glass order parameter, and magnetizations, and discuss about the phase transition phenomena. Experimental results roughly indicated that the phase of 3-SAT problem in hard-SAT condition and low temperature circumstances is mixed phase (magnetization is non-zero and replica symmetry breaking (RSB) occurs), but it needs further validation.
Keyword (in Japanese) (See Japanese page) 
(in English) K-satisfiability (K-SAT) problem / exchange Monte Carlo method / principal component analysis (PCA) / replica symmetry breaking (RSB) / / / /  
Reference Info. IEICE Tech. Rep., vol. 111, no. 194, IBISML2011-37, pp. 165-172, Sept. 2011.
Paper # IBISML2011-37 
Date of Issue 2011-08-29 (PRMU, IBISML) 
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)
Download PDF PRMU2011-78 IBISML2011-37

Conference Information
Conference Date 2011-09-05 - 2011-09-06 
Place (in Japanese) (See Japanese page) 
Place (in English)  
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Paper Information
Registration To IBISML 
Conference Code 2011-09-PRMU-IBISML-CVIM 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Visualization of the Phase Transition Phenomena on K-satisfiability Problem through Principal Component Analysis 
Sub Title (in English)  
Keyword(1) K-satisfiability (K-SAT) problem  
Keyword(2) exchange Monte Carlo method  
Keyword(3) principal component analysis (PCA)  
Keyword(4) replica symmetry breaking (RSB)  
1st Author's Name Yasuaki Akazawa  
1st Author's Affiliation Waseda University (Waseda Univ.)
2nd Author's Name Masato Okada  
2nd Author's Affiliation The University of Tokyo (Univ. Tokyo)
3rd Author's Name Masato Inoue  
3rd Author's Affiliation Waseda University (Waseda Univ.)
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Date Time 2011-09-06 15:20:00 
Presentation Time 30 
Registration for IBISML 
Paper # IEICE-PRMU2011-78,IEICE-IBISML2011-37 
Volume (vol) IEICE-111 
Number (no) no.193(PRMU), no.194(IBISML) 
Page pp.165-172 
#Pages IEICE-8 
Date of Issue IEICE-PRMU-2011-08-29,IEICE-IBISML-2011-08-29 

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