Fast Distributed Algorithms for Testing Graph Properties

Censor-Hillel, Keren; Fischer, Eldar; Schwartzman, Gregory; Vasudev, Yadu

doi:10.1007/978-3-662-53426-7_4

Cited by 15 publications

(2 citation statements)

References 35 publications

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“…Property testing algorithms for triangle-freeness were given by Censor-Hillel et al [8]; for H-freeness for graphs on 4 nodes by Fraigniaud et al [19] and Even et al [15]; and for H-freeness for most graphs on 5 nodes by Fischer et al [16] Moreover, property testing algorithms for tree and cycle freeness-using techniques of fixed-parameter algorithmics flavour-have been discovered recently [14][15][16]19].…”

Section: Related Workmentioning

confidence: 99%

“…In this work, we study this problem in the CONGEST model of distributed computation. So far, most work has either focused on (a) lower bounds for subgraph detection [12], (b) randomised upper bounds [16,20], or (c) property testing of H-freeness [8,16,18]. By contrast, we focus on deterministic upper bounds, showing that simple techniques-indeed, often techniques well-known in non-distributed algorithmics-result in essentially optimal algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic subgraph detection in broadcast CONGEST

Korhonen,

Rybicki

2017

Preprint

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We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation:-For any constant k, detecting k-paths and trees on k nodes can be done in O(1) rounds.-For any constant k, detecting k-cycles and pseudotrees on k nodes can be done in O(n) rounds.-On d-degenerate graphs, cliques and 4-cycles can be enumerated in O(d + log n) rounds, and 5-cycles in O(d 2 + log n) rounds.In many cases, these bounds are tight up to logarithmic factors. Moreover, we show that the algorithms for d-degenerate graphs can be improved to optimal complexity O(d/ log n) and O(d 2 / log n), respectively, in the supported CONGEST model, which can be seen as an intermediate model between CONGEST and the congested clique.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deterministic subgraph detection in broadcast CONGEST

Korhonen,

Rybicki

2017

Preprint

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On a Verification Framework for Certifying Distributed Algorithms: Distributed Checking and Consistency

Völlinger

Akili

2018

Formal Techniques for Distributed Objects, Components, and Systems

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A major problem in software engineering is assuring the correctness of a distributed system. A certifying distributed algorithm (CDA) computes for its input-output pair (i, o) an additional witness w -a formal argument for the correctness of (i, o). Each CDA features a witness predicate such that if the witness predicate holds for a triple (i, o, w), the input-output pair (i, o) is correct. An accompanying checker algorithm decides the witness predicate. Consequently, a user of a CDA does not have to trust the CDA but its checker algorithm. Usually, a checker is simpler and its verification is feasible. To sum up, the idea of a CDA is to adapt the underlying algorithm of a program at design-time such that it verifies its own output at runtime. While certifying sequential algorithms are well-established, there are open questions on how to apply certification to distributed algorithms. In this paper, we discuss distributed checking of a distributed witness; one challenge is that all parts of a distributed witness have to be consistent with each other. Furthermore, we present a method for formal instance verification (i.e. obtaining a machine-checked proof that a particular input-output pair is correct), and implement the method in a framework for the theorem prover Coq.

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Distributed Testing of Excluded Subgraphs

Fraigniaud

Rapaport

Salo

et al. 2016

Lecture Notes in Computer Science

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International audienceWe study property testing in the context of distributed computing , under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. We show that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds too. The constant also depends on how far the input graph is from being H-free, and the dependence is identical to the one in the case of testing triangle-freeness. Hence, in particular, testing whether a graph is K4-free, and testing whether a graph is C4-free can be done in a constant number of rounds (where K k denotes the k-node clique, and C k denotes the k-node cycle). On the other hand, we show that testing K k-freeness and C k-freeness for k ≥ 5 appear to be much harder. Specifically , we investigate two natural types of generic algorithms for testing H-freeness, called DFS tester and BFS tester. The latter captures the previously known algorithm to test the presence of triangles, while the former captures our generic algorithm to test the presence of a 4-node graph pattern H. We prove that both DFS and BFS testers fail to test K k-freeness and C k-freeness in a constant number of rounds for k ≥ 5

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Fast Distributed Algorithms for Testing Graph Properties

Cited by 15 publications

References 35 publications

Deterministic subgraph detection in broadcast CONGEST

Deterministic subgraph detection in broadcast CONGEST

On a Verification Framework for Certifying Distributed Algorithms: Distributed Checking and Consistency

Distributed Testing of Excluded Subgraphs

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