Local certification of graphs with bounded genus

Naor, Parter, and Yogev [SODA 2020] recently designed a compiler for automatically translating standard centralized interactive protocols to distributed protocols, as introduced by Kol, Oshman, Saxena [PODC 2018]. In particular, using this compiler, every linear-time algorithm deciding the membership some fixed graph class can be translated into dMAM(O(logn)) protocol class, that is, with O(logn)-bit proof size in n-node graphs, three interactions between (centralized) computationally-unbounded but non-trustable prover Merlin, (decentralized) randomized computationally-limited verifier Arthur. As corollary, there is recognizing of planar well graphs bounded genus. We show exists genus performing just single interaction, from verifier, yet preserving O(logn) bits. This result also holds non-orientable genus, embedded on surface The described paper are actually proof-labeling schemes, i.e., subclass previously Korman, Kutten, Peleg 2005]. these schemes do not require any randomization proofs may often computed priori, at low cost, nodes themselves. Our results thus extend recent scheme Feuilloley et al. 2020],