Compact Distributed Certification of Planar Graphs

Naor M., Parter M., Yogev E.: (The power of distributed verifiers in interactive proofs. In: 31st ACM-SIAM symposium on discrete algorithms (SODA), pp 1096–115, 2020. https://doi.org/10.1137/1.9781611975994.67 ) have recently demonstrated the existence of a distributed interactive proof for planarit...

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Veröffentlicht in:Algorithmica Jg. 83; H. 7; S. 2215 - 2244
Hauptverfasser: Feuilloley, Laurent, Fraigniaud, Pierre, Montealegre, Pedro, Rapaport, Ivan, Rémila, Éric, Todinca, Ioan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2021
Springer Nature B.V
Springer Verlag
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Certificates
Certification
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Algorithms
Data Structures and Information Theory
IP (Internet Protocol)
Labeling
Mathematics of Computing
Randomization
Theory of Computation
Network algorithms
Planarity
Distributed algorithms
Graph property certification
Labeling schemes
ISSN:0178-4617, 1432-0541
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Zusammenfassung:Naor M., Parter M., Yogev E.: (The power of distributed verifiers in interactive proofs. In: 31st ACM-SIAM symposium on discrete algorithms (SODA), pp 1096–115, 2020. https://doi.org/10.1137/1.9781611975994.67 ) 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 with 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.
Bibliographie:ObjectType-Article-1
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-021-00823-w