Classification of Distributed Binary Labeling Problems

Alkida Balliu, Brandt Sebastian, Yuval Efron, Juho Hirvonen, Yannic Maus, Dennis Olivetti, Jukka Suomela

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Abstract

We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two in the edge labeling formalism. Examples of binary labeling problems include sinkless orientation, sinkless and sourceless orientation, 2-vertex coloring, perfect matching, and the task of coloring edges red and blue such that all nodes are incident to at least one red and at least one blue edge. More generally, we can encode e.g. any cardinality constraints on indegrees and outdegrees. We study the deterministic time complexity of solving a given binary labeling problem in trees, in the usual LOCAL model of distributed computing. We show that the complexity of any such problem is in one of the following classes: O(1), Θ(log n), Θ(n), or unsolvable. In particular, a problem that can be represented in the binary labeling formalism cannot have time complexity Θ(log^* n), and hence we know that e.g. any encoding of maximal matchings has to use at least three labels (which is tight). Furthermore, given the description of any binary labeling problem, we can easily determine in which of the four classes it is and what is an asymptotically optimal algorithm for solving it. Hence the distributed time complexity of binary labeling problems is decidable, not only in principle, but also in practice: there is a simple and efficient algorithm that takes the description of a binary labeling problem and outputs its distributed time complexity.
Original languageEnglish
Title of host publication34th International Symposium on Distributed Computing (DISC 2020)
EditorsHagit Attiya
Chapter17
Number of pages17
ISBN (Electronic)978-3-95977-168-9
DOIs
Publication statusPublished - 2020
MoE publication typeA4 Article in a conference publication
EventInternational Symposium on Distributed Computing - Virtual, Online, Germany
Duration: 12 Oct 202016 Oct 2020
Conference number: 32
http://www.disc-conference.org/wp/disc2020/

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum für Informatik
Volume179
ISSN (Electronic)1868-8969

Conference

ConferenceInternational Symposium on Distributed Computing
Abbreviated titleDISC
CountryGermany
CityVirtual, Online
Period12/10/202016/10/2020
Internet address

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