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| Presentation | 2007-06-29 09:00 A Computaional Complexity for finding a Maximum Clique in a Graph with Maximum Degree 4 Hiroaki Nakanishi, Etsuji Tomita (UEC)  COMP2007-18 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The maximum clique problem is an NP-hard problem, and is difficult to solve efficiently. The trivial upper bound of its time complexity is O(P(n)2^n), where P(n) is a polynomial of n, the number of vertices. Several improvements have been done for this upper bound. In this note, we present a simple branch-and-bound algorithm for the maximum clique problem. It is based on our preceeding algorithm CLIQUES, which is designed for generating all maximal cliques. We aim to prove that our algorithm improves the upper bound for finding a maximum clique in a general graph, and we show here that it has O(n^3) upper bound in a graph with maximum degree 4, as a basis of the analysis for a general case. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | NP-hard / Maximum clique / Maiximum independent set / Time complexity / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 107, no. 127, COMP2007-18, pp. 1-7, June 2007. | |
| Paper # | COMP2007-18 | |
| Date of Issue | 2007-06-22 (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) | |
| Download PDF | COMP2007-18 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2007-06-29 - 2007-06-29 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Hokkaido University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2007-06-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A Computaional Complexity for finding a Maximum Clique in a Graph with Maximum Degree 4 |
| Sub Title (in English) | |
| Keyword(1) | NP-hard |
| Keyword(2) | Maximum clique |
| Keyword(3) | Maiximum independent set |
| Keyword(4) | Time complexity |
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| 1st Author's Name | Hiroaki Nakanishi |
| 1st Author's Affiliation | The University of Electro-Communications (UEC) |
| 2nd Author's Name | Etsuji Tomita |
| 2nd Author's Affiliation | The University of Electro-Communications (UEC) |
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| Speaker | Author-1 |
| Date Time | 2007-06-29 09:00:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | COMP2007-18 |
| Volume (vol) | vol.107 |
| Number (no) | no.127 |
| Page | pp.1-7 |
| #Pages | 7 |
| Date of Issue | 2007-06-22 (COMP) |
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