Fast distributed algorithms for testing graph properties

We initiate a thorough study of distributed property testing —producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called dense graph testing model we emulate sequential tests for nearly all graph properties having 1-sided tests, whi...

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Bibliographic Details
Published in:Distributed computing Vol. 32; no. 1; pp. 41 - 57
Main Authors: Censor-Hillel, Keren, Fischer, Eldar, Schwartzman, Gregory, Vasudev, Yadu
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2019
Springer Nature B.V
Subjects:
Algorithms
Computer Communication Networks
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Lower bounds
Machinery
Model testing
Properties (attributes)
Run time (computers)
Software Engineering/Programming and Operating Systems
Task complexity
Theory of Computation
Testing Bipartiteness
Proof Labeling Schemes
Dense Graph Model
Induced Subgraph
Property Testing
ISSN:0178-2770, 1432-0452
Online Access:Get full text
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Summary:We initiate a thorough study of distributed property testing —producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called dense graph testing model we emulate sequential tests for nearly all graph properties having 1-sided tests, while in the general model we obtain faster tests for triangle-freeness and cycle-freeness, and in the sparse model we obtain a faster test for bipartiteness. In addition, we show a logarithmic lower bound for testing bipartiteness and cycle-freeness, which holds even in the stronger LOCAL model. In most cases, aided by parallelism, the distributed algorithms have a much shorter running time than their counterparts from the sequential querying model of traditional property testing. More importantly, the distributed algorithms we develop for testing graph properties are in many cases much faster than what is known for exactly deciding whether the property holds. The simplest property testing algorithms allow a relatively smooth transition to the distributed model. For the more complex tasks we develop new machinery that may be of independent interest.
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ISSN:0178-2770
1432-0452
DOI:10.1007/s00446-018-0324-8