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| Presentation | 2010-12-03 16:35 Maximum Domination Problem Eiji Miyano (Kyushu Inst. of Tech.), Hirotaka Ono (Kyushu Univ.)  COMP2010-46 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | We consider new variants of the vertex/edge domination problems on graphs. A vertex is said to {\em dominate} itself and its all adjacent vertices, and similarly an edge is said to {\em dominate} itself and its all adjacent edges. Given an input graph $G = (V, E)$ and an integer $k$, the {\sc $k$-Vertex ($k$-Edge) Maximum Domination} ({\sf $k$-MaxVD} and {\sf $k$-MaxED}, respectively) is to find a subset $D_{V} \subseteq V$ of vertices (resp., $D_{E}\subseteq E$ of edges) with size at most $k$ that maximizes the cardinality of dominated vertices (resp., edges). In this paper, we first show that a simple greedy strategy achieves an approximation ratio of $(1-1/e)$ for both {\sf $k$-MaxVD} and {\sf $k$-MaxED}. Then, we show that this approximation ratio is the best possible for {\sf $k$-MaxVD} unless ${\cal P} = {\cal NP}$. We also prove that, for any constant $\varepsilon > 0$, there is no polynomial time $1303/1304 + \varepsilon$ approximation algorithm for {\sf $k$-MaxED} unless ${\cal P} = {\cal NP}$. However, if $k$ is not larger than the size of the minimum maximal matching, {\sf $k$-MaxED} is $3/4$-approximable in polynomial time. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Dominating set / Approximation algorithm / Inapproximability / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 110, no. 325, COMP2010-46, pp. 53-60, Dec. 2010. | |
| Paper # | COMP2010-46 | |
| Date of Issue | 2010-11-26 (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 | COMP2010-46 |
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| 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 | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Maximum Domination Problem |
| Sub Title (in English) | |
| Keyword(1) | Dominating set |
| Keyword(2) | Approximation algorithm |
| Keyword(3) | Inapproximability |
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| 1st Author's Name | Eiji Miyano |
| 1st Author's Affiliation | Kyushu Institute of Technology (Kyushu Inst. of Tech.) |
| 2nd Author's Name | Hirotaka Ono |
| 2nd Author's Affiliation | Kyushu university (Kyushu Univ.) |
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| Speaker | 2 |
| Date Time | 2010-12-03 16:35:00 |
| Presentation Time | 35 |
| Registration for | COMP |
| Paper # | IEICE-COMP2010-46 |
| Volume (vol) | IEICE-110 |
| Number (no) | no.325 |
| Page | pp.53-60 |
| #Pages | IEICE-8 |
| Date of Issue | IEICE-COMP-2010-11-26 |
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