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Faster Graph Algorithms Through DAG Compression

Authors Max Bannach , Florian Andreas Marwitz , Till Tantau

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Author Details

Max Bannach
  • European Space Agency, Advanced Concepts Team, Noordwijk, The Netherlands
Florian Andreas Marwitz
  • Institute of Information Systems, Universität zu Lübeck, Germany
Till Tantau
  • Institute for Theoretical Computer Science, Universität zu Lübeck, Germany

Funding

  • Marwitz, Florian Andreas: The research for this paper was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2176 "Understanding Written Artefacts: Material, Interaction and Transmission in Manuscript Cultures", project no. 390893796. The research was conducted within the scope of the Centre for the Study of Manuscript Cultures (CSMC) at Universität Hamburg.

Cite AsGet BibTex

Max Bannach, Florian Andreas Marwitz, and Till Tantau. Faster Graph Algorithms Through DAG Compression. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.STACS.2024.8

Abstract

The runtime of graph algorithms such as depth-first search or Dijkstra’s algorithm is dominated by the fact that all edges of the graph need to be processed at least once, leading to prohibitive runtimes for large, dense graphs. We introduce a simple data structure for storing graphs (and more general structures) in a compressed manner using directed acyclic graphs (dags). We then show that numerous standard graph problems can be solved in time linear in the size of the dag compression of a graph, rather than in the number of edges of the graph. Crucially, many dense graphs, including but not limited to graphs of bounded twinwidth, have a dag compression of size linear in the number of vertices rather than edges. This insight allows us to improve the previous best results for the runtime of standard algorithms from quasi-linear to linear for the large class of graphs of bounded twinwidth, which includes all cographs, graphs of bounded treewidth, or graphs of bounded cliquewidth.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • graph compression
  • graph traversal
  • twinwidth
  • parameterized algorithms

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