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Faster Fully Dynamic Transitive Closure in Practice

Authors Kathrin Hanauer , Monika Henzinger , Christian Schulz

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Kathrin Hanauer
  • University of Vienna, Faculty of Computer Science, Austria
Monika Henzinger
  • University of Vienna, Faculty of Computer Science, Austria
Christian Schulz
  • University of Vienna, Faculty of Computer Science, Austria

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Kathrin Hanauer, Monika Henzinger, and Christian Schulz. Faster Fully Dynamic Transitive Closure in Practice. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 14:1-14:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been thoroughly investigated in theory and many specialized algorithms for solving it have been proposed in the last decades. In two large studies [Frigioni ea, 2001; Krommidas and Zaroliagis, 2008], a number of these algorithms have been evaluated experimentally against simple, static algorithms for graph traversal, showing the competitiveness and even superiority of the simple algorithms in practice, except for very dense random graphs or very high ratios of queries. A major drawback of those studies is that only small and mostly randomly generated graphs are considered. In this paper, we engineer new algorithms to maintain all-pairs reachability information which are simple and space-efficient. Moreover, we perform an extensive experimental evaluation on both generated and real-world instances that are several orders of magnitude larger than those in the previous studies. Our results indicate that our new algorithms outperform all state-of-the-art algorithms on all types of input considerably in practice.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Dynamic Graph Algorithms
  • Reachability
  • Transitive Closure


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