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Paper Abstract and Keywords
Presentation 2021-03-08 11:30
[Invited Talk] Tight Distributed Listing of Cliques
Keren Censor-Hillel (Technion), Yi-Jun Chang (ETH), François Le Gall (Nagoya Univ.), Dean Leitersdorf (Technion) COMP2020-31
Abstract (in Japanese) (See Japanese page) 
(in English) Much progress has recently been made in understanding the complexity landscape of subgraph finding problems in the CONGEST model of distributed computing. However, so far, very few tight bounds are known in this area. For triangle (i.e., 3-clique) listing, an optimal $tilde{O}(n^{1/3})$-round distributed algorithm has been constructed by Chang et al. [SODA 2019, PODC 2019]. Recent works have shown sublinear algorithms for $K_p$-listing, for each $p geq 4$, but still leaving a significant gap between the upper bounds and the known lower bounds of the problem.

In this work, we completely close this gap. We show that for each $p geq 4$, there is an $tilde{O}(n^{1 - 2/p})$-round distributed algorithm that lists all $p$-cliques $K_p$ in the communication network. Our algorithm is optimal up to a polylogarithmic factor, due to the $tilde{Omega}(n^{1 - 2/p})$-round lower bound of Fischer et al. [SPAA 2018], which holds even in the CONGESTED CLIQUE model. Together with the triangle-listing algorithm by Chang et al. [SODA 2019, PODC 2019], our result thus shows that the round complexity of $K_p$-listing, for all $p$, is the same in both the CONGEST and CONGESTED CLIQUE models, at $tilde{Theta}(n^{1 - 2/p})$ rounds.

For $p=4$, our result additionally matches the $tilde{Omega}(n^{1/2})$ lower bound for $K_4$-emph{detection} by Czumaj and Konrad [DISC 2018], implying that the round complexities for detection and listing of $K_4$ are equivalent in the CONGEST model.
Keyword (in Japanese) (See Japanese page) 
(in English) Distributed computing / Distributed algorithms / Graph problems / Cliques / / / /  
Reference Info. IEICE Tech. Rep., vol. 120, no. 426, COMP2020-31, pp. 24-24, March 2021.
Paper # COMP2020-31 
Date of Issue 2021-03-01 (COMP) 
ISSN 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 COMP2020-31

Conference Information
Committee COMP  
Conference Date 2021-03-08 - 2021-03-08 
Place (in Japanese) (See Japanese page) 
Place (in English) Online 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2021-03-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Tight Distributed Listing of Cliques 
Sub Title (in English)  
Keyword(1) Distributed computing  
Keyword(2) Distributed algorithms  
Keyword(3) Graph problems  
Keyword(4) Cliques  
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1st Author's Name Keren Censor-Hillel  
1st Author's Affiliation Technion (Technion)
2nd Author's Name Yi-Jun Chang  
2nd Author's Affiliation ETH (ETH)
3rd Author's Name François Le Gall  
3rd Author's Affiliation Nagoya University (Nagoya Univ.)
4th Author's Name Dean Leitersdorf  
4th Author's Affiliation Technion (Technion)
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Speaker Author-3 
Date Time 2021-03-08 11:30:00 
Presentation Time 60 minutes 
Registration for COMP 
Paper # COMP2020-31 
Volume (vol) vol.120 
Number (no) no.426 
Page p.24 
#Pages 1 
Date of Issue 2021-03-01 (COMP) 

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