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Distributed Detection of Cycles

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Abstract

Distributed property testing in networks has been introduced by Brakerski and Patt-Shamir (2011), with the objective of detecting the presence of large dense sub-networks in a distributed manner. Recently, Censor-Hillel et al. (2016) have shown how to detect 3-cycles in a constant number of rounds by a distributed algorithm. In a follow up work, Fraigniaud et al. (2016) have shown how to detect 4-cycles in a constant number of rounds as well. However, the techniques in these latter works were shown not to generalize to larger cycles Ck with k ≥ 5. In this paper, we completely settle the problem of cycle detection, by establishing the following result. For every k ≥ 3, there exists a distributed property testing algorithm for Ck-freeness, performing in a constant number of rounds. All these results hold in the classical congest/ model for distributed network computing. Our algorithm is 1-sided error. Its round-complexity is O(1/ε) where ε ∈(0,1) is the property testing parameter measuring the gap between legal and illegal instances.

Dates and versions

hal-01674646 , version 1 (03-01-2018)

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Pierre Fraigniaud, Olivetti Dennis. Distributed Detection of Cycles. SPAA 2017 - 29th ACM Symposium on Parallelism in Algorithms and Architectures, Jul 2017, Washington, United States. pp.153-162, ⟨10.1145/3087556.3087571⟩. ⟨hal-01674646⟩
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