Efficient Labeling for Reachability in Directed Acyclic Graphs

Authors Maciej Dulęba, Paweł Gawrychowski, Wojciech Janczewski

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Maciej Dulęba
  • Institute of Computer Science, University of Wrocław, Poland
Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland
Wojciech Janczewski
  • Institute of Computer Science, University of Wrocław, Poland

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Maciej Dulęba, Paweł Gawrychowski, and Wojciech Janczewski. Efficient Labeling for Reachability in Directed Acyclic Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • informative labeling scheme
  • reachability
  • DAG


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