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Paper Abstract and Keywords
Presentation 2017-12-21 11:25
O(n^{1/3})-space algorithm for the grid graph reachability problem
Ryo Ashida, Kotaro Nakagawa (Tokyo Tech) ISEC2017-75 COMP2017-29
Abstract (in Japanese) (See Japanese page) 
(in English) The directed graph reachability problem is a canonical complete problem for class NL.
The best known polynomial time algorithm for this problem by Barns et al. uses $O(n/2^{sqrt{log{n}}})$ space.
Whether we can make $O(n^eps)$-space and polynomial time algorithm for some $eps < 1$ is a famous open problem.
For some restricted graph classes of directed graphs, better results are known.
Asano et al. gave an $widetilde{O}(sqrt{n})$ space and polynomial time algorithm for the reachability problem restricted to directed grid and planar graphs.
We propose an $widetilde{O}(n^{1/3})$ space and polynomial time algorithm for the reachability problem restricted to directed grid graphs.
Keyword (in Japanese) (See Japanese page) 
(in English) graph algorithm / graph reachability / grid graph / sub-linear space algorithm / / / /  
Reference Info. IEICE Tech. Rep., vol. 117, no. 370, COMP2017-29, pp. 19-24, Dec. 2017.
Paper # COMP2017-29 
Date of Issue 2017-12-14 (ISEC, 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 ISEC2017-75 COMP2017-29

Conference Information
Committee ISEC COMP  
Conference Date 2017-12-21 - 2017-12-22 
Place (in Japanese) (See Japanese page) 
Place (in English) Eikokuji Campus, Kochi University of Technology 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2017-12-ISEC-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) O(n^{1/3})-space algorithm for the grid graph reachability problem 
Sub Title (in English)  
Keyword(1) graph algorithm  
Keyword(2) graph reachability  
Keyword(3) grid graph  
Keyword(4) sub-linear space algorithm  
1st Author's Name Ryo Ashida  
1st Author's Affiliation Tokyo Institute of Technology (Tokyo Tech)
2nd Author's Name Kotaro Nakagawa  
2nd Author's Affiliation Tokyo Institute of Technology (Tokyo Tech)
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Speaker Author-1 
Date Time 2017-12-21 11:25:00 
Presentation Time 25 minutes 
Registration for COMP 
Paper # ISEC2017-75, COMP2017-29 
Volume (vol) vol.117 
Number (no) no.369(ISEC), no.370(COMP) 
Page pp.19-24 
Date of Issue 2017-12-14 (ISEC, COMP) 

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