The Simultaneous Number-in-Hand Communication Model for Networks: Private Coins, Public Coins and Determinism

Becker, Florent; Montealegre, Pedro; Rapaport, Ivan; Todinca, Ioan

doi:10.1007/978-3-319-09620-9_8

Cited by 15 publications

(14 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, if instead of bounding the number of rounds we bound the message size b, then the best known result is the following: detecting deterministically a triangle requires Ω(n/(e O( √ log n b)) rounds [7]. In [5], the authors consider three variants of the broadcast congested clique model: randomized protocols with public coins, randomized protocols with private coins and deterministic protocols. They showed that this choice affects the message size complexity of some problems.…”

Section: Related Workmentioning

confidence: 97%

See 1 more Smart Citation

Brief Announcement

Becker¹,

Anta

Rapaport

et al. 2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

Self Cite

View full text Add to dashboard Cite

The CON GEST model is a synchronous, message-passing model of distributed computation in which each node can send (possibly different) messages of O(log n) bits along each of its incident communication links in each round, where n is the number of computing nodes in the system. In the particular case where the communication network is a complete graph, we have the unicast congested clique model. On the other end is the broadcast version of the congested clique model, in which each node can only broadcast a single message over all its links in each round. In this paper we explore the space, in terms of round complexity, that lies between these two congested clique models. Hence, we parametrize the congested clique model with the range r, the maximum number of different messages a node can send over its incident links in one round. Additionally, we study the effect of the bandwidth b, the maximum size in bits of these messages.We show that the space between the unicast and broadcast congested clique models is very rich and interesting. For instance, we show that a problem (especially designed for this work) takes Ω(n/ log n) rounds in the broadcast model (r = 1), while it can be solved in two rounds if two messages can be sent (r = 2). Other gaps are found in other parts of the spectrum of values of r. We do this by providing techniques to simulate protocols with different parameters.

show abstract

Section: Related Workmentioning

confidence: 97%

“…This setting is equivalent to the multi-party, number-inhand computation model, where communication takes place in a shared whiteboard [1,2,3,4,5,7]: writing a message M on the whiteboard is equivalent to broadcasting M.…”

Section: Introductionmentioning

confidence: 99%

Brief Announcement

Becker¹,

Anta

Rapaport

et al. 2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

Self Cite

View full text Add to dashboard Cite

show abstract

“…Claim 1. Let T be a tree satisfying (2). Then, one can chose r ∈ T as the root of T such that Proof of Claim 1.…”

Section: Leaderless Nodes In Large Components: Proof Of Propmentioning

confidence: 99%

“…Then, one can chose r ∈ T as the root of T such that Proof of Claim 1. Let r 0 be an arbitrary node of a tree T which satisfies (2). If (a) is satisfied for r = r 0 , we are done.…”

Section: Leaderless Nodes In Large Components: Proof Of Propmentioning

confidence: 99%

MST in O(1) Rounds of Congested Clique

Jurdziński¹,

Nowicki²

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

We present a distributed randomized algorithm finding Minimum Spanning Tree (MST) of a given graph in O(1) rounds, with high probability, in the congested clique model.The input graph in the congested clique model is a graph of n nodes, where each node initially knows only its incident edges. The communication graph is a clique with limited edge bandwidth: each two nodes (not necessarily neighbours in the input graph) can exchange O(log n) bits.As in previous works, the key part of the MST algorithm is an efficient Connected Components (CC) algorithm. However, unlike the former approaches, we do not aim at simulating the standard Boruvka's algorithm, at least at initial stages of the CC algorithm. Instead, we develop a new technique which combines connected components of sample sparse subgraphs of the input graph in order to accelerate the process of uncovering connected components of the original input graph. More specifically, we develop a sparsification technique which reduces an initial CC problem in O(1) rounds to its two restricted instances. The former instance has a graph with maximal degree

show abstract

“…In [7] the authors prove that it is impossible to decide whether the input graph G has diameter at most 3 or whether G has a triangle unless the messages sent by the nodes are all of size Ω(n), even if randomness is allowed. Deciding whether the input graph G contains a cycle requires at least one node to write a message of length at least log d − 1, where d is the maximum degree of G [4].…”

Section: Introductionmentioning

confidence: 99%

Solving the Induced Subgraph Problem in the Randomized Multiparty Simultaneous Messages Model

Kari

Matamala

Rapaport

et al. 2015

Structural Information and Communication Complexity

Self Cite

View full text Add to dashboard Cite

Abstract. We study the message size complexity of recognizing, under the broadcast congested clique model, whether a fixed graph H appears in a given graph G as a minor, as a subgraph or as an induced subgraph. The n nodes of the input graph G are the players, and each player only knows the identities of its immediate neighbors. We are mostly interested in the one-round, simultaneous setup where each player sends a message of size O(log n) to a referee that should be able then to determine whether H appears in G. We consider randomized protocols where the players have access to a common random sequence. We completely characterize which graphs H admit such a protocol. For the particular case where H is the path of 4 nodes, we present a new notion called twin ordering, which may be of independent interest.

show abstract

The Simultaneous Number-in-Hand Communication Model for Networks: Private Coins, Public Coins and Determinism

Cited by 15 publications

References 11 publications

Brief Announcement

Brief Announcement

MST in O(1) Rounds of Congested Clique

Solving the Induced Subgraph Problem in the Randomized Multiparty Simultaneous Messages Model

Contact Info

Product

Resources

About