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Fast Reachability Using DAG Decomposition

Authors Giorgos Kritikakis , Ioannis G. Tollis

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Giorgos Kritikakis
  • Univeristy of Crete, Heraklion, Greece
Ioannis G. Tollis
  • Univeristy of Crete, Heraklion, Greece

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Giorgos Kritikakis and Ioannis G. Tollis. Fast Reachability Using DAG Decomposition. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.SEA.2023.2

Abstract

We present a fast and practical algorithm to compute the transitive closure (TC) of a directed graph. It is based on computing a reachability indexing scheme of a directed acyclic graph (DAG), G = (V, E). Given any path/chain decomposition of G we show how to compute in parameterized linear time such a reachability scheme that can answer reachability queries in constant time. The experimental results reveal that our method is significantly faster in practice than the theoretical bounds imply, indicating that path/chain decomposition algorithms can be applied to obtain fast and practical solutions to the transitive closure (TC) problem. Furthermore, we show that the number of non-transitive edges of a DAG G is ≤ width*|V| and that we can find a substantially large subset of the transitive edges of G in linear time using a path/chain decomposition. Our extensive experimental results show the interplay between these concepts in various models of DAGs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • Theory of computation → Design and analysis of algorithms
Keywords
  • graph algorithms
  • hierarchy
  • directed acyclic graphs (DAG)
  • path/chain decomposition
  • transitive closure
  • transitive reduction
  • reachability
  • reachability indexing scheme

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