Explicit Space-Time Tradeoffs for Proof Labeling Schemes in Graphs with Small Separators

Orr Fischer, Rotem Oshman, Dana Shamir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In distributed verification, our goal is to verify that the network configuration satisfies some desired property, using pre-computed information stored at each network node. This is formally modeled as a proof labeling scheme (PLS): a prover assigns to each node a certificate, and then the nodes exchange their certificates with their neighbors and decide whether to accept or reject the configuration. Subsequent work has shown that in some specific cases, allowing more rounds of communication – so that nodes can communicate further across the network – can yield shorter certificates, trading off the space required to store the certificate against the time required for verification. Such tradeoffs were previously known for trees, cycles, and grids, or for proof labeling schemes where all nodes receive the same certificate. In this work we show that in large classes of graphs, every one-round PLS can be transformed into a multi-round PLS with shorter certificates. We give two constructions: given a 1-round PLS with certificates of ℓ bits, in graphs families with balanced edge separators of size s(n), we construct a t-round PLS with certificates of size Õ(ℓ · s(n)/t), and in graph families with an excluded minor and maximum degree ∆, we construct a t-round PLS with certificates of size Õ(ℓ · ∆/t). Our constructions are explicit, and we use erasure codes to exploit the larger neighborhood viewed by each node in a t-round PLS.

Original languageEnglish
Title of host publication25th International Conference on Principles of Distributed Systems, OPODIS 2021
EditorsQuentin Bramas, Vincent Gramoli, Vincent Gramoli, Alessia Milani
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772198
DOIs
StatePublished - 1 Feb 2022
Event25th International Conference on Principles of Distributed Systems, OPODIS 2021 - Strasbourg, France
Duration: 13 Dec 202115 Dec 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume217
ISSN (Print)1868-8969

Conference

Conference25th International Conference on Principles of Distributed Systems, OPODIS 2021
Country/TerritoryFrance
CityStrasbourg
Period13/12/2115/12/21

Keywords

  • Families with excluded minor
  • Proof-labeling schemes
  • Space-time tradeoffs

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