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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 
Bitar, N.; Goles, E.; Montealegre, P. 


Title 
COMPUTATIONAL COMPLEXITY OF BIASED DIFFUSIONLIMITED AGGREGATION 
Type 


Year 
2022 
Publication 
Siam Journal On Discrete Mathematics 
Abbreviated Journal 
SIAM Discret. Math. 


Volume 
36 
Issue 
1 
Pages 
823866 


Keywords 
diffusionlimited aggregation; computational complexity; space complexity; NLcompleteness; Pcompleteness 


Abstract 
DiffusionLimited Aggregation (DLA) is a clustergrowth model that consists in a set of particles that are sequentially aggregated over a twodimensional grid. In this paper, we introduce a biased version of the DLA model, in which particles are limited to move in a subset of possible directions. We denote by kDLA the model where the particles move only in k possible directions. We study the biased DLA model from the perspective of Computational Complexity, defining two decision problems The first problem is Prediction, whose input is a site of the grid c and a sequence S of walks, representing the trajectories of a set of particles. The question is whether a particle stops at site c when sequence S is realized. The second problem is Realization, where the input is a set of positions of the grid, P. The question is whether there exists a sequence S that realizes P, i.e. all particles of S exactly occupy the positions in P. Our aim is to classify the Prediciton and Realization problems for the different versions of DLA. We first show that Prediction is PComplete for 2DLA (thus for 3DLA). Later, we show that Prediction can be solved much more efficiently for 1DLA. In fact, we show that in that case the problem is NLComplete. With respect to Realization, we show that restricted to 2DLA the problem is in P, while in the 1DLA case, the problem is in L. 


Address 



Corporate Author 

Thesis 



Publisher 

Place of Publication 

Editor 



Language 

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:000778502000037 
Approved 



Call Number 
UAI @ alexi.delcanto @ 
Serial 
1558 

Permanent link to this record 