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Author (up) Becker, F.; Montealecre, P.; Rapaport, I.; Todinca, I. doi  openurl
  Title The Impact Of Locality In The Broadcast Congested Clique Model Type Journal Article
  Year 2020 Publication Siam Journal On Discrete Mathematics Abbreviated Journal SIAM Discret. Math.  
  Volume 34 Issue 1 Pages 682-700  
  Keywords broadcast congested clique; induced cycles; graph degeneracy  
  Abstract The broadcast congested clique model (BCLIQUE) is a message-passing model of distributed computation where n nodes communicate with each other in synchronous rounds. First, in this paper we prove that there is a one-round, deterministic algorithm that reconstructs the input graph G if the graph is d-degenerate, 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 one-round algorithm that solves CYCLE>k needs the bandwidth b to be at least Omega(n/ log n). We also show the existence of a one-round, 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 epsilon-error, R-round, b-bandwidth 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@univ-orleans.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 0895-4801 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000546886700033 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 1182  
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