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

Kari, Jarkko; Matamala, Martı́n; Rapaport, Ivan; Salo, Ville

doi:10.1007/978-3-319-25258-2_26

Cited by 15 publications

(13 citation statements)

References 26 publications

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“…Moreover, conjectures about the time complexity of triangle detection and of its variants [1-3, 28, 64] are among the cornerstones of fine-grained complexity (see [63]). Other highly non-trivial algorithms were designed for it in settings such as: distributed models [15,16,21,22,25,30,32], quantum computing [11,14,38,[40][41][42]47,61], and Map-Reduce [4,58]. It is truly remarkable that such a basic problem has lead to so much research.…”

Section: Introductionmentioning

confidence: 99%

Fooling views: a new lower bound technique for distributed computations under congestion

et al. 2020

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We introduce a novel lower bound technique for distributed graph algorithms under bandwidth limitations. We define the notion of fooling views and exemplify its strength by proving two new lower bounds for triangle membership in the Congest(B) model:1. Any 1-round algorithm requires B ≥ c∆ log n for a constant c > 0.2. If B = 1, even in constant-degree graphs any algorithm must take Ω(log * n) rounds.The implication of the former is the first proven separation between the Local and the Congest models for deterministic triangle membership. The latter result is the first non-trivial lower bound on the number of rounds required, even for triangle detection, under limited bandwidth. All previous known techniques are provably incapable of giving these bounds. We hope that our approach may pave the way for proving lower bounds for additional problems in various settings of distributed computing for which previous techniques do not suffice.

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Section: Introductionmentioning

confidence: 99%

Fooling views: a new lower bound technique for distributed computations under congestion

et al. 2020

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“…This class is obviously hereditary. In [16], the authors presented a one-round public-coin algorithm that solves…”

Section: Related Workmentioning

confidence: 99%

Graph Reconstruction in the Congested Clique

Montealegre¹,

Perez-Salazar²,

Rapaport³

et al. 2017

Preprint

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The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of n nodes. In this paper we consider the situation where the joint input to the nodes is an nnode labeled graph G, i.e., the local input received by each node is the indicator function of its neighborhood in G. Nodes execute an algorithm, communicating with each other in synchronous rounds and their goal is to compute some function that depends on G. In every round, each of the n nodes may send up to n − 1 different b-bit messages through each of its n − 1 communication links. We denote by R the number of rounds of the algorithm. The product Rb, that is, the total number of bits received by a node through one link, is the cost of the algorithm.The most difficult problem we could attempt to solve is the reconstruction problem, where nodes are asked to recover all the edges of the input graph G. Formally, given a class of graphs G, the problem is defined as follows: if G / ∈ G, then every node must reject; on the other hand, if G ∈ G, then every node must end up, after the R rounds, knowing all the edges of G. It is not difficult to see that the cost Rb of any algorithm that solves this problem (even with public coins) is at least Ω(log |G n |/n), where G n is the subclass of all n-node labeled graphs in G. In this paper we prove that previous bound is tight and that it is possible to achieve it with only R = 2 rounds. More precisely, we exhibit (i) a one-round algorithm that achieves this bound for hereditary graph classes; and (ii) a two-round algorithm that achieves this bound for arbitrary graph classes. Later, we show that the bound Ω(log |G n |/n) cannot be achieved in one-round for arbitrary graph classes, and we give tight algorithms for that case.From (i) we recover all known results concerning the reconstruction of graph classes in one round and bandwidth O(log n): forests, planar graphs, cographs, etc. But we also get new one-round algorithms for other hereditary graph classes such as unit disc graphs, interval graphs, etc. From (ii), we can conclude that any problem restricted to a class of graphs of size 2 O(n log n) can be solved in the congested clique model in two rounds, with bandwidth O(log n). Moreover, our general two-round algorithm is valid for any set of labeled graphs, not only for graph classes (which are sets of labeled graphs closed under isomorphims).

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“…Variants of the model are also considered, in which problems such as deciding triangle-freeness or connectivity are considered. See also [49] for deciding the presence of induced subgraphs.…”

Section: General Interpretation Of Individual Outputsmentioning

confidence: 99%

Survey of Distributed Decision

Feuilloley,

Fraigniaud

2016

Preprint

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We survey the recent distributed computing literature on checking whether a given distributed system configuration satisfies a given boolean predicate, i.e., whether the configuration is legal or illegal w.r.t. that predicate. We consider classical distributed computing environments, including mostly synchronous fault-free network computing (LOCAL and CON-GEST models), but also asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile computing (FSYNC model).

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

Cited by 15 publications

References 26 publications

Fooling views: a new lower bound technique for distributed computations under congestion

Fooling views: a new lower bound technique for distributed computations under congestion

Graph Reconstruction in the Congested Clique

Survey of Distributed Decision

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