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Author 
Becker, F.; Montealecre, P.; Rapaport, I.; Todinca, I. 


Title 
The Impact Of Locality In The Broadcast Congested Clique Model 
Type 


Year 
2020 
Publication 
Siam Journal On Discrete Mathematics 
Abbreviated Journal 
SIAM Discret. Math. 


Volume 
34 
Issue 
1 
Pages 
682700 


Keywords 
broadcast congested clique; induced cycles; graph degeneracy 


Abstract 
The broadcast congested clique model (BCLIQUE) is a messagepassing model of distributed computation where n nodes communicate with each other in synchronous rounds. First, in this paper we prove that there is a oneround, deterministic algorithm that reconstructs the input graph G if the graph is ddegenerate, and rejects otherwise, using bandwidth b = O(d . log n). Then, we introduce a new parameter to the model. We study the situation where the nodes, initially, instead of knowing their immediate neighbors, know their neighborhood up to a fixed radius r. In this new framework, denoted BCLIQuE[r], we study the problem of detecting, in G, an induced cycle of length at most k (CYCLE <= k) and the problem of detecting an induced cycle of length at least k +1 (CYCLE>k). We give upper and lower bounds. We show that if each node is allowed to see up to distance r = left perpendicular k/2 right perpendicular + 1, then a polylogarithmic bandwidth is sufficient for solving CYCLE>k with only two rounds. Nevertheless, if nodes were allowed to see up to distance r = left perpendicular k/3 right perpendicular, then any oneround algorithm that solves CYCLE>k needs the bandwidth b to be at least Omega(n/ log n). We also show the existence of a oneround, deterministic BCLIQUE algorithm that solves CYCLE <= k with bandwitdh b = O(n(1/left perpendicular k/2 right perpendicular). log n). On the negative side, we prove that, if epsilon <= 1/3 and 0 < r <= k/4, then any epsilonerror, Rround, bbandwidth algorithm in the BCLIQUE[r] model that solves problem CYCLE(<= k )satisfies R . b = Omega(n(1/left perpendicular k/2 right perpendicular)). 


Address 
[Becker, F.; Todinca, I] Univ Orleans, INSA Ctr Val Loire, LIFO EA 4022, Orleans, France, Email: florent.becker@univorleans.fr; 


Corporate Author 

Thesis 



Publisher 
Siam Publications 
Place of Publication 

Editor 



Language 
English 
Summary Language 

Original Title 



Series Editor 

Series Title 

Abbreviated Series Title 



Series Volume 

Series Issue 

Edition 



ISSN 
08954801 
ISBN 

Medium 



Area 

Expedition 

Conference 



Notes 
WOS:000546886700033 
Approved 



Call Number 
UAI @ eduardo.moreno @ 
Serial 
1182 

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Author 
Montealegre, R.; PerezSalazar, S.; Rapaport, I.; Todinca, I. 


Title 
Graph reconstruction in the congested clique 
Type 


Year 
2020 
Publication 
Journal Of Computer And System Sciences 
Abbreviated Journal 
J. Comput. Syst. Sci. 


Volume 
113 
Issue 

Pages 
117 


Keywords 
Distributed computing; Congested clique; Round complexity; Reconstruction problem; Graph classes 


Abstract 
In this paper we study the reconstruction problem in the congested clique model. Given a class of graphs g, the problem is defined as follows: if G is not an element of g, then every node must reject; if G is an element of g, then every node must end up knowing all the edges of G. The cost of an algorithm is the total number of bits received by any node through one link. It is not difficult to see that the cost of any algorithm that solves this problem is Omega(log vertical bar g(n)vertical bar/n), where g(n) is the subclass of all nnode labeled graphs in g. We prove that the lower bound is tight and that it is possible to achieve it with only 2 rounds. (C) 2020 Elsevier Inc. All rights reserved. 


Address 
[Montealegre, R.] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: p.montealegre@edu.uai; 


Corporate Author 

Thesis 



Publisher 
Academic Press Inc Elsevier Science 
Place of Publication 

Editor 



Language 
English 
Summary Language 

Original Title 



Series Editor 

Series Title 

Abbreviated Series Title 



Series Volume 

Series Issue 

Edition 



ISSN 
00220000 
ISBN 

Medium 



Area 

Expedition 

Conference 



Notes 
WOS:000539435200001 
Approved 



Call Number 
UAI @ eduardo.moreno @ 
Serial 
1190 

Permanent link to this record 