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Paper Abstract and Keywords
Presentation 2010-12-03 14:30
An improved result on polynomial-time solvability of the maximum clique problem
Hiroaki Nakanishi, Etsuji Tomita (UEC) COMP2010-43
Abstract (in Japanese) (See Japanese page) 
(in English) This report presents an improved result for polynomial-time solvability of the maximum clique problem which is a typical NP complete problem.
That is:
for a graph with n vertices, if the maximum degree Δ is less than or equal to 2.613dlg n (d ≧ 1: a constant), then
the maximum clique problem is solvable in the polynomial
time of O(n^{1+d}).
In particular, in case $d=1$, the time complexity of O(n^{2}) is optimal with respect to the number n of vertices .
This is a direct improvement of our preceding result in Trans. IEICE, vol.J93-D, no.4, pp.417--425.
Such an improvement has been achieved by introducing a new technique to
successfully reduce the search space.
Keyword (in Japanese) (See Japanese page) 
(in English) NP-Complete / Maximum Clique / Depth-First Search / Time-Complexity / Maximum Degree / / /  
Reference Info. IEICE Tech. Rep., vol. 110, no. 325, COMP2010-43, pp. 29-36, Dec. 2010.
Paper # COMP2010-43 
Date of Issue 2010-11-26 (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)
Download PDF COMP2010-43

Conference Information
Committee COMP  
Conference Date 2010-12-03 - 2010-12-03 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyutech Plaza, Kyushu Institute of Technology 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2010-12-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) An improved result on polynomial-time solvability of the maximum clique problem 
Sub Title (in English)  
Keyword(1) NP-Complete  
Keyword(2) Maximum Clique  
Keyword(3) Depth-First Search  
Keyword(4) Time-Complexity  
Keyword(5) Maximum Degree  
1st Author's Name Hiroaki Nakanishi  
1st Author's Affiliation University of Electro-Communications (UEC)
2nd Author's Name Etsuji Tomita  
2nd Author's Affiliation University of Electro-Communications (UEC)
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Date Time 2010-12-03 14:30:00 
Presentation Time 35 
Registration for COMP 
Paper # IEICE-COMP2010-43 
Volume (vol) IEICE-110 
Number (no) no.325 
Page pp.29-36 
#Pages IEICE-8 
Date of Issue IEICE-COMP-2010-11-26 

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