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Randomized proof-labeling schemes

Abstract : Proof-labeling schemes, introduced by Korman et al. (Distrib Comput 22(4):215–233, 2010. https://doi.org/10.1007/s00446-010-0095-3), are a mechanism to certify that a network configuration satisfies a given boolean predicate. Such mechanisms find applications in many contexts, e.g., the design of fault-tolerant distributed algorithms. In a proof-labeling scheme, predicate verification consists of neighbors exchanging labels, whose contents depends on the predicate. In this paper, we introduce the notion of randomized proof-labeling schemes where messages are randomized and correctness is probabilistic. We show that randomization reduces verification complexity exponentially while guaranteeing probability of correctness arbitrarily close to one. We also present a novel message-size lower bound technique that applies to deterministic as well as randomized proof-labeling schemes. Using this technique, we establish several tight bounds on the verification complexity of MST, acyclicity, connectivity, and longest cycle size.
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https://hal.inria.fr/hal-02433478
Contributor : Pierre Fraigniaud <>
Submitted on : Thursday, January 9, 2020 - 10:33:29 AM
Last modification on : Friday, April 10, 2020 - 5:14:28 PM

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Pierre Fraigniaud, Boaz Patt-Shamir, Mor Perry. Randomized proof-labeling schemes. Distributed Computing, Springer Verlag, 2019, 32 (3), pp.217-234. ⟨10.1007/s00446-018-0340-8⟩. ⟨hal-02433478⟩

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