Proof Labeling Schemes for Reachability-Related Problems in Directed Graphs

Yoav Ben Shimon, Orr Fischer, Rotem Oshman

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

Abstract

We study proof labeling schemes in directed networks, and ask what assumptions are necessary to be able to certify reachability-related problems such as strong connectivity, or the existence of a node from which all nodes are reachable. In contrast to undirected networks, in directed networks, having unique identifiers alone does not suffice to be able to certify all graph properties; thus, we study the effect of knowing the size of the graph, and of each node knowing its out-degree. We formalize the notion of giving the nodes initial knowledge about the network, and give tight characterizations of the types of knowledge that are necessary and sufficient to certify several reachability-related properties, or to be able to certify any graph property. For example, we show that in order to certify that the network contains a node that is reachable from all nodes, it is necessary and sufficient to have any two of the assumptions we study (unique identifiers, knowing the size, or knowing the out-degree); and to certify strong connectivity, it is necessary and sufficient to have any single assumption.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings
EditorsMerav Parter
PublisherSpringer Science and Business Media Deutschland GmbH
Pages21-41
Number of pages21
ISBN (Print)9783031099922
DOIs
StatePublished - 2022
Event29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022 - Paderborn, Germany
Duration: 27 Jun 202229 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13298 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022
Country/TerritoryGermany
CityPaderborn
Period27/06/2229/06/22

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