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 Paper Abstract and Keywords Presentation 2010-12-03 16:35 Maximum Domination ProblemEiji Miyano (Kyushu Inst. of Tech.), Hirotaka Ono (Kyushu Univ.) COMP2010-46 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. 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 Copyrightandreproduction 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

 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 Keyword(4) Keyword(5) Keyword(6) Keyword(7) Keyword(8) 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.) 3rd Author's Name 3rd Author's Affiliation () 4th Author's Name 4th Author's Affiliation () 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () 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