2026-07-25T03:06:51Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13371 2024-03-06T10:51:49Z ddc:004 open_access

Efficient Labeling for Reachability in Directed Acyclic Graphs Dulęba, Maciej Gawrychowski, Paweł Janczewski, Wojciech informative labeling scheme reachability DAG We consider labeling nodes of a directed graph for reachability queries. A reachability labeling scheme for such a graph assigns a binary string, called a label, to each node. Then, given the labels of nodes u and v and no other information about the underlying graph, it should be possible to determine whether there exists a directed path from u to v. By a simple information theoretical argument and invoking the bound on the number of partial orders, in any scheme some labels need to consist of at least n/4 bits, where n is the number of nodes. On the other hand, it is not hard to design a scheme with labels consisting of n/2+𝒪(log n) bits. In the classical centralised setting, where a single data structure is stored as a whole, Munro and Nicholson designed a structure for reachability queries consisting of n²/4+o(n²) bits (which is optimal, up to the lower order term). We extend their approach to obtain a scheme with labels consisting of n/3+o(n) bits. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Maciej Dulęba and Paweł Gawrychowski and Wojciech Janczewski 2020 Is Part Of LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2020.27 urn:nbn:de:0030-drops-133710 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.27 eng https://creativecommons.org/licenses/by/3.0/legalcode