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Distributed Detection of Cycles

Pierre Fraigniaud 1, 2 Dennis Olivetti 1
2 GANG - Networks, Graphs and Algorithms
IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale, Inria de Paris
Abstract : Distributed property testing in networks has been introduced by Brakerski and Patt-Shamir [6], with the objective of detecting the presence of large dense sub-networks in a distributed manner. Recently, Censor-Hillel et al. [7] have revisited this notion and formalized it in a broader context. In particular, they 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. [21] 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 article, 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(1ϵ) where ϵ ∈ (0,1) is the property-testing parameter measuring the gap between legal and illegal instances.
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Submitted on : Thursday, January 9, 2020 - 10:37:56 AM
Last modification on : Tuesday, January 11, 2022 - 11:16:04 AM

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Pierre Fraigniaud, Dennis Olivetti. Distributed Detection of Cycles. ACM Transactions on Parallel Computing, Association for Computing Machinery, 2019, 6 (3), pp.1-20. ⟨10.1145/3322811⟩. ⟨hal-02433486⟩



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