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Paper Abstract and Keywords
Presentation 2010-12-03 16:35
Maximum Domination Problem
Eiji 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
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
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  
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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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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