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Author Montealegre, R.; Perez-Salazar, S.; Rapaport, I.; Todinca, I. doi  openurl
  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 1-17  
  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 n-node 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 0022-0000 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000539435200001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1229  
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Author Montealegre, R.; Perez-Salazar, S.; Rapaport, I.; Todinca, I. doi  openurl
  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 1-17  
  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 n-node 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 0022-0000 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000539435200001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1190  
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Author Becker, F.; Montealecre, P.; Rapaport, I.; Todinca, I. doi  openurl
  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 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  
  Call Number UAI @ eduardo.moreno @ Serial 1182  
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Author Liedloff, M.; Montealegre, P.; Todinca, I. doi  openurl
  Title Beyond Classes of Graphs with “Few” Minimal Separators: FPT Results Through Potential Maximal Cliques Type
  Year 2019 Publication Algorithmica Abbreviated Journal Algorithmica  
  Volume 81 Issue 3 Pages 986-1005  
  Keywords FPT algorithms; Treewidth; Potential maximal cliques  
  Abstract Let P(G,X) be a property associating a boolean value to each pair (G,X) where G is a graph and X is a vertex subset. Assume that P is expressible in counting monadic second order logic (CMSO) and let t be an integer constant. We consider the following optimization problem: given an input graph G=(V,E), find subsets XFV such that the treewidth of G[F] is at most t, property P(G[F],X) is true and X is of maximum size under these conditions. The problem generalizes many classical algorithmic questions, e.g., Longest Induced Path, Maximum Induced Forest, IndependentH-Packing, etc. Fomin et al. (SIAM J Comput 44(1):54-87, 2015) proved that the problem is polynomial on the class of graph Gpoly, i.e. the graphs having at most poly(n) minimal separators for some polynomial poly. Here we consider the class Gpoly+kv, formed by graphs of Gpoly to which we add a set of at most k vertices with arbitrary adjacencies, called modulator. We prove that the generic optimization problem is fixed parameter tractable on Gpoly+kv, with parameter k, if the modulator is also part of the input.  
  Address [Liedloff, Mathieu; Todinca, Ioan] Univ Orleans, INSA Ctr Val Loire, LIFO, EA 4022, Orleans, France, Email: mathieu.liedloff@univ-orleans.fr;  
  Corporate Author Thesis  
  Publisher Springer Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0178-4617 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000460105700003 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 989  
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Author Becker, F.; Kosowski, A.; Matamala, M.; Nisse, N.; Rapaport, I.; Suchan, K.; Todinca, I. pdf  doi
openurl 
  Title Allowing each node to communicate only once in a distributed system: shared whiteboard models Type
  Year 2015 Publication Distributed Computing Abbreviated Journal Distrib. Comput.  
  Volume 28 Issue 3 Pages 189-200  
  Keywords Distributed computing; Local computation; Graph properties; Bounded communication  
  Abstract In this paper we study distributed algorithms on massive graphs where links represent a particular relationship between nodes (for instance, nodes may represent phone numbers and links may indicate telephone calls). Since such graphs are massive they need to be processed in a distributed way. When computing graph-theoretic properties, nodes become natural units for distributed computation. Links do not necessarily represent communication channels between the computing units and therefore do not restrict the communication flow. Our goal is to model and analyze the computational power of such distributed systems where one computing unit is assigned to each node. Communication takes place on a whiteboard where each node is allowed to write at most one message. Every node can read the contents of the whiteboard and, when activated, can write one small message based on its local knowledge. When the protocol terminates its output is computed from the final contents of the whiteboard. We describe four synchronization models for accessing the whiteboard. We show that message size and synchronization power constitute two orthogonal hierarchies for these systems. We exhibit problems that separate these models, i.e., that can be solved in one model but not in a weaker one, even with increased message size. These problems are related to maximal independent set and connectivity. We also exhibit problems that require a given message size independently of the synchronization model.  
  Address [Becker, Florent; Todinca, Ioan] Univ Orleans, LIFO, Orleans, France, Email: florent.becker@univ-orleans.fr;  
  Corporate Author Thesis  
  Publisher Springer Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0178-2770 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000354708400003 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 492  
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Author Goles, E.; Montealegre-Barba, P.; Todinca, I. pdf  doi
openurl 
  Title The complexity of the bootstraping percolation and other problems Type
  Year 2013 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.  
  Volume 504 Issue Pages 73-82  
  Keywords  
  Abstract We study the problem of predicting the state of a vertex in automata networks, where the state at each site is given by the majority function over its neighborhood. We show that for networks with maximum degree greater than 5 the problem is P-Complete, simulating a monotone Boolean circuit. Then, we show that the problem for networks with no vertex with degree greater than 4 is in NC, giving a fast parallel algorithm. Finally, we apply the result to the study of related problems. (C) 2012 Elsevier B.V. All rights reserved.  
  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 0304-3975 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000325905100008 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 320  
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Author Rapaport, I.; Suchan, K.; Todinca, I.; Verstraete, J. pdf  doi
openurl 
  Title On Dissemination Thresholds in Regular and Irregular Graph Classes Type
  Year 2011 Publication Algorithmica Abbreviated Journal Algorithmica  
  Volume 59 Issue 1 Pages 16-34  
  Keywords Bootstrap percolation; Cubic graphs; Information dissemination  
  Abstract We investigate the natural situation of the dissemination of information on various graph classes starting with a random set of informed vertices called active. Initially active vertices are chosen independently with probability p, and at any stage in the process, a vertex becomes active if the majority of its neighbours are active, and thereafter never changes its state. This process is a particular case of bootstrap percolation. We show that in any cubic graph, with high probability, the information will not spread to all vertices in the graph if p < 1/2. We give families of graphs in which information spreads to all vertices with high probability for relatively small values of p.  
  Address [Todinca, I.] Univ Orleans, LIFO, Orleans, France, Email: rapaport@dim.uchile.cl  
  Corporate Author Thesis  
  Publisher Springer Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0178-4617 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000286525300003 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 119  
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