Compact Distributed Certification of Planar Graphs

Feuilloley, Laurent; Fraigniaud, Pierre; Montealegre, Pedro; Rapaport, Ivan; Remila, Eric; Todinca, Ioan


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. 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.

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Título según WOS: Compact Distributed Certification of Planar Graphs
Título de la Revista: ALGORITHMICA
Volumen: 83
Número: 7
Editorial: Springer
Fecha de publicación: 2021
Página de inicio: 2215
Página final: 2244


Notas: ISI