research-article

Local certification of graphs with bounded genus

Authors:

Laurent Feuilloley,

Pierre Fraigniaud,

Pedro Montealegre,

Ioan TodincaAuthors Info & Claims

Volume 325, Issue C

Pages 9 - 36

https://doi.org/10.1016/j.dam.2022.10.004

Published: 30 January 2023 Publication History

Abstract

Naor, Parter, and Yogev [SODA 2020] recently designed a compiler for automatically translating standard centralized interactive protocols to distributed interactive protocols, as introduced by Kol, Oshman, and Saxena [PODC 2018]. In particular, by using this compiler, every linear-time algorithm for deciding the membership to some fixed graph class can be translated into a dMAM ( O ( log n ) ) protocol for this class, that is, a distributed interactive protocol with O ( log n )-bit proof size in n-node graphs, and three interactions between the (centralized) computationally-unbounded but non-trustable prover Merlin, and the (decentralized) randomized computationally-limited verifier Arthur. As a corollary, there is a dMAM ( O ( log n ) ) protocol for recognizing the class of planar graphs, as well as for recognizing the class of graphs with bounded genus.

We show that there exists a distributed interactive protocol for recognizing the class of graphs with bounded genus performing just a single interaction, from the prover to the verifier, yet preserving proof size of O ( log n ) bits. This result also holds for the class of graphs with bounded non-orientable genus, that is, graphs that can be embedded on a non-orientable surface of bounded genus. The interactive protocols described in this paper are actually proof-labeling schemes, i.e., a subclass of interactive protocols, previously introduced by Korman, Kutten, and Peleg [PODC 2005]. In particular, these schemes do not require any randomization from the verifier, and the proofs may often be computed a priori, at low cost, by the nodes themselves. Our results thus extend the recent proof-labeling scheme for planar graphs by Feuilloley et al. [PODC 2020], to graphs of bounded genus, and to graphs of bounded non-orientable genus.

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Cited By

Fomin FFraigniaud PMontealegre PRapaport ITodinca IKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Distributed Model Checking on Graphs of Bounded TreedepthProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662793(205-208)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662793
Feuilloley LJanoušek JKřišťan JSedláček J(2024)Decreasing Verification Radius in Local CertificationAlgorithmics of Wireless Networks10.1007/978-3-031-74580-5_14(188-201)Online publication date: 5-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-74580-5_14

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Local certification of graphs with bounded genus
1. Software and its engineering
2. Theory of computation

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cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 325, Issue C

Jan 2023

309 pages

ISSN:0166-218X

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Elsevier B.V.

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Elsevier Science Publishers B. V.

Netherlands

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Published: 30 January 2023

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Cited By

Fomin FFraigniaud PMontealegre PRapaport ITodinca IKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Distributed Model Checking on Graphs of Bounded TreedepthProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662793(205-208)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662793
Feuilloley LJanoušek JKřišťan JSedláček J(2024)Decreasing Verification Radius in Local CertificationAlgorithmics of Wireless Networks10.1007/978-3-031-74580-5_14(188-201)Online publication date: 5-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-74580-5_14

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