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Fast Reachability Using DAG Decomposition

Authors Giorgos Kritikakis , Ioannis G. Tollis

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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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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.

Cite As Get BibTex

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

Author Details

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

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References

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