Compact Distributed Certification of Planar Graphs

Laurent Feuilloley, Pierre Fraigniaud, Ivan Rapaport, Éric Rémila, Pedro Montealegre, Ioan Todinca.

PODC 2020: 39th ACM Symposium on Principles of Distributed Computing, 3-7 August 2020, Virtual event, Italy
doi: 10.1145/3382734.3404505


Journal version Publisher's version


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(logn) 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(logn) bits. We also show that there are no proof-labeling schemes -- in fact, even no locally checkable proofs -- for planarity using certificates on o(logn) bits.


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