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Paper Abstract and Keywords
Presentation 2009-10-16 10:35
Small Grid Drawings of Planar Graphs with Balanced Bipartition
Xiao Zhou, Takashi Hikino, Takao Nishizeki (Tohoku Univ.) COMP2009-33
Abstract (in Japanese) (See Japanese page) 
(in English) In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It has been known that every planar graph $G$ of $n$ vertices has a grid drawing on an $(n-2)\times (n-2)$ integer grid and such a drawing can be found in linear time. In this paper we show that if a planar graph $G$ has a balanced bipartition then $G$ has a grid drawing with small grid area. More precisely, if a separation pair bipartitions $G$ into two edge-disjoint subgraphs $G_1$ and $G_2$, then $G$ has a grid drawing on a $W\times H$ grid such that both the width $W$ and height $H$ are smaller than the larger number of vertices in $G_1$ and in $G_2$. In particular, we show that every series-parallel graph $G$ has a grid drawing on a $(2n/3)\times (2n/3)$ grid and such a drawing can be found in linear time.
Keyword (in Japanese) (See Japanese page) 
(in English) grid drawing / series-parallel graph / planar graph / / / / /  
Reference Info. IEICE Tech. Rep., vol. 109, no. 235, COMP2009-33, pp. 9-15, Oct. 2009.
Paper # COMP2009-33 
Date of Issue 2009-10-09 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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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)
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Conference Information
Committee COMP  
Conference Date 2009-10-16 - 2009-10-16 
Place (in Japanese) (See Japanese page) 
Place (in English) Tohoku University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2009-10-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Small Grid Drawings of Planar Graphs with Balanced Bipartition 
Sub Title (in English)  
Keyword(1) grid drawing  
Keyword(2) series-parallel graph  
Keyword(3) planar graph  
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1st Author's Name Xiao Zhou  
1st Author's Affiliation Tohoku University (Tohoku Univ.)
2nd Author's Name Takashi Hikino  
2nd Author's Affiliation Tohoku University (Tohoku Univ.)
3rd Author's Name Takao Nishizeki  
3rd Author's Affiliation Tohoku University (Tohoku Univ.)
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Speaker Author-2 
Date Time 2009-10-16 10:35:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2009-33 
Volume (vol) vol.109 
Number (no) no.235 
Page pp.9-15 
#Pages
Date of Issue 2009-10-09 (COMP) 


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