Adding a Referee to an Interconnection Network: What Can(not) Be Computed in One Round

Becker, Florent; Matamala, Martı́n; Nisse, Nicolas; Rapaport, Ivan; Suchan, Karol; Todinca, Ioan

doi:10.1109/ipdps.2011.55

Cited by 22 publications

(44 citation statements)

References 25 publications

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“…For instance, [2] proves that deciding if a graph has degeneracy k, k ≥ 1, can be solved in SimAsync[log n]. On the negative side, deciding whether a graph contains a triangle as a subgraph and deciding whether a graph has diameter at most 3 cannot be solved in SimAsync[log n] [2].…”

Section: Asynchronous Protocolsmentioning

confidence: 99%

“…The computation the nodes need to perform collectively is related to some property of the graph. In [2] the first simple model for studying such scenario was introduced. In that model, the total amount of local information that each node was allowed to provide was bounded by O(log n) bits.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we define extensions of the model in [2] and investigate their computational power. It is interesting to point out that despite being extremely natural, these models of computation have never been studied before.…”

Section: Introductionmentioning

confidence: 99%

“…The computational model in [2] can be stated equivalently in the following form. Given a question about the graph, every node writes simultaneously one message (computed from its local knowledge) on a global zone of shared memory, a whiteboard, and then one must be able to answer the question using only the contents of the whiteboard.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we intend to give more power to the initial model of [2]. For this purpose, we relax the simultaneity constraint in different ways.…”

Section: Introductionmentioning

confidence: 99%

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Allowing each node to communicate only once in a distributed system: shared whiteboard models

et al. 2014

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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 and streaming 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.

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Section: Asynchronous Protocolsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In this paper we intend to give more power to the initial model of [2]. For this purpose, we relax the simultaneity constraint in different ways.…”

Section: Introductionmentioning

confidence: 99%

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Allowing each node to communicate only once in a distributed system: shared whiteboard models

et al. 2014

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Robust reconstruction of Barabási‐Albert networks in the broadcast congested clique model

et al. 2015

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In the broadcast version of the congested clique model, n nodes communicate in synchronous rounds by writing O(log n)-bit messages on a whiteboard, which is visible to all of them. The joint input to the nodes is an undirected n-node graph G, with node i receiving the list of its neighbors in G. Our goal is to design a protocol at the end of which the information contained in the whiteboard is enough for reconstructing G. It has already been shown that there is a one-round protocol for reconstructing graphs with bounded degeneracy. The main drawback of that protocol is that the degeneracy m of the input graph G must be known a priori by the nodes. Moreover, the protocol fails when applied to graphs with degeneracy larger than m. In this paper we address this issue by looking for robust reconstruction protocols, that is, protocols which always give the correct answer and work efficiently when the input is restricted to a certain class. We introduce a very simple, two-round protocol that we call Robust-Reconstruction. We prove that this protocol is robust for reconstructing the class of Barabási-Albert trees with (expected) message size O(log n). Moreover, we present computational evidence suggesting that Robust-Reconstruction also generates logarithmic size messages for arbitrary Barabási-Albert networks. Finally, we stress the importance of the preferential attachment mechanism (used in the construction of Barabási-Albert networks) by proving that RobustReconstruction does not generate short messages for random recursive 1 trees.

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Two Rounds Are Enough for Reconstructing Any Graph (Class) in the Congested Clique Model

Montealegre¹,

Perez-Salazar²,

Rapaport³

et al. 2018

Structural Information and Communication Complexity

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Adding a Referee to an Interconnection Network: What Can(not) Be Computed in One Round

Cited by 22 publications

References 25 publications

Allowing each node to communicate only once in a distributed system: shared whiteboard models

Allowing each node to communicate only once in a distributed system: shared whiteboard models

Robust reconstruction of Barabási‐Albert networks in the broadcast congested clique model

Two Rounds Are Enough for Reconstructing Any Graph (Class) in the Congested Clique Model

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