Amortized \(\tilde{O}(|V|)\)-Delay Algorithm for Listing Chordless Cycles in Undirected Graphs

  • Rui Ferreira
  • Roberto Grossi
  • Romeo Rizzi
  • Gustavo Sacomoto
  • Marie-France Sagot
Conference paper

DOI: 10.1007/978-3-662-44777-2_35

Volume 8737 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Ferreira R., Grossi R., Rizzi R., Sacomoto G., Sagot MF. (2014) Amortized \(\tilde{O}(|V|)\)-Delay Algorithm for Listing Chordless Cycles in Undirected Graphs. In: Schulz A.S., Wagner D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg

Abstract

Chordless cycles are very natural structures in undirected graphs, with an important history and distinguished role in graph theory. Motivated also by previous work on the classical problem of listing cycles, we study how to list chordless cycles. The best known solution to list all the C chordless cycles contained in an undirected graph G = (V,E) takes O(|E|2 + |E| ·C) time. In this paper we provide an algorithm taking \(\tilde{O}(|E| + |V| \cdot C)\) time. We also show how to obtain the same complexity for listing all the P chordless st-paths in G (where C is replaced by P).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Rui Ferreira
    • 1
  • Roberto Grossi
    • 2
  • Romeo Rizzi
    • 3
  • Gustavo Sacomoto
    • 4
    • 5
  • Marie-France Sagot
    • 4
    • 5
  1. 1.Microsoft BingUK
  2. 2.Università di PisaItaly
  3. 3.Università di VeronaItaly
  4. 4.INRIA Grenoble Rhône-AlpesFrance
  5. 5.UMR CNRS 5558 - LBBE, Université Lyon 1France