research-article

Compact Distributed Certification of Planar Graphs

Authors:

Laurent Feuilloley,

Pierre Fraigniaud,

Pedro Montealegre,

Ioan TodincaAuthors Info & Claims

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

Pages 319 - 328

https://doi.org/10.1145/3382734.3404505

Published: 31 July 2020 Publication History

Abstract

Naor, Parter, and Yogev (SODA 2020) have recently demonstrated the existence of a distributed interactive proof for planarity (i.e., for certifying that a network is planar), using a sophisticated generic technique for constructing distributed IP protocols based on sequential IP protocols. The interactive proof for planarity is based on a distributed certification of the correct execution of any given sequential linear-time algorithm for planarity testing. It involves three interactions between the prover and the randomized distributed verifier (i.e., it is a dMAM protocol), and uses small certificates, on O(log n) bits in n-node networks. We show that a single interaction from the prover suffices, and randomization is unecessary, by providing an explicit description of a proof-labeling scheme for planarity, still using certificates on just O(log n) bits. We also show that there are no proof-labeling schemes --- in fact, even no locally checkable proofs --- for planarity using certificates on o(log n) bits.

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Cited By

Maldonado DMontealegre PRíos-Wilson M(2024)The Hardness of Local Certification of Finite-State DynamicsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_4(51-65)Online publication date: 6-Mar-2024
https://doi.org/10.1007/978-3-031-55598-5_4
Maldonado DMontealegre PRíos-Wilson MTheyssier G(2024)Local Certification of Majority DynamicsSOFSEM 2024: Theory and Practice of Computer Science10.1007/978-3-031-52113-3_26(369-382)Online publication date: 7-Feb-2024
https://doi.org/10.1007/978-3-031-52113-3_26
Esperet LLévêque B(2022)Local certification of graphs on surfacesTheoretical Computer Science10.1016/j.tcs.2022.01.023Online publication date: Jan-2022
https://doi.org/10.1016/j.tcs.2022.01.023
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Index Terms

Compact Distributed Certification of Planar Graphs
1. Networks
  1. Network algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms
    2. Graph algorithms analysis

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cover image ACM Conferences

PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing

July 2020

539 pages

ISBN:9781450375825

DOI:10.1145/3382734

General Chair:
Yuval Emek
Technion, Israel
,
Program Chair:
Christian Cachin
University of Bern, Switzerland

Copyright © 2020 ACM.

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Published: 31 July 2020

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Cited By

Maldonado DMontealegre PRíos-Wilson M(2024)The Hardness of Local Certification of Finite-State DynamicsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_4(51-65)Online publication date: 6-Mar-2024
https://doi.org/10.1007/978-3-031-55598-5_4
Maldonado DMontealegre PRíos-Wilson MTheyssier G(2024)Local Certification of Majority DynamicsSOFSEM 2024: Theory and Practice of Computer Science10.1007/978-3-031-52113-3_26(369-382)Online publication date: 7-Feb-2024
https://doi.org/10.1007/978-3-031-52113-3_26
Esperet LLévêque B(2022)Local certification of graphs on surfacesTheoretical Computer Science10.1016/j.tcs.2022.01.023Online publication date: Jan-2022
https://doi.org/10.1016/j.tcs.2022.01.023
Jauregui BMontealegre PRapaport I(2022)Distributed Interactive Proofs for the Recognition of Some Geometric Intersection Graph ClassesStructural Information and Communication Complexity10.1007/978-3-031-09993-9_12(212-233)Online publication date: 25-Jun-2022
https://doi.org/10.1007/978-3-031-09993-9_12

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