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

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Algorithms - ESA 2014 (ESA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8737))

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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).

GS and MFS were partially supported by the ERC programme FP7/2007-2013 / ERC grant agreement no. [247073]10, and the French project ANR-12-BS02-0008 (Colib’read). RG was partially supported by Italian project PRIN 2012C4E3KT (AMANDA).

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Author information

Authors and Affiliations

  1. Microsoft Bing, UK

    Rui Ferreira

  2. Università di Pisa, Italy

    Roberto Grossi

  3. Università di Verona, Italy

    Romeo Rizzi

  4. INRIA Grenoble Rhône-Alpes, France

    Gustavo Sacomoto & Marie-France Sagot

  5. UMR CNRS 5558 - LBBE, Université Lyon 1, France

    Gustavo Sacomoto & Marie-France Sagot

Authors
  1. Rui Ferreira
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  2. Roberto Grossi
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  3. Romeo Rizzi
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  4. Gustavo Sacomoto
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  5. Marie-France Sagot
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Editor information

Editors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Andreas S. Schulz

  2. Karlsruhe Institute of Technology (KIT), Kaiserstruhe 12, 76131, Karlsruhe, Germany

    Dorothea Wagner

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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. https://doi.org/10.1007/978-3-662-44777-2_35

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  • DOI: https://doi.org/10.1007/978-3-662-44777-2_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44776-5

  • Online ISBN: 978-3-662-44777-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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