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Random Generation and Enumeration of Proper Interval Graphs

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WALCOM: Algorithms and Computation (WALCOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5431))

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Abstract

We investigate connected proper interval graphs without vertex labels. We first give the number of connected proper interval graphs of n vertices. Using it, a simple algorithm that generates a connected proper interval graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected proper interval graphs is proposed. The algorithm is based on the reverse search, and it outputs each connected proper interval graph in \(\mbox{\cal O}(1)\) time.

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Author information

Authors and Affiliations

  1. School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa, 923-1292, Japan

    Toshiki Saitoh, Masashi Kiyomi & Ryuhei Uehara

  2. Graduate School of Information Systems, The University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo, 182-8585, Japan

    Katsuhisa Yamanaka

Authors
  1. Toshiki Saitoh
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  2. Katsuhisa Yamanaka
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  3. Masashi Kiyomi
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  4. Ryuhei Uehara
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Editor information

Editors and Affiliations

  1. Indian Statistical Institute, 700 108, Kolkata, India

    Sandip Das

  2. Japan Advanced Institute of Science and Technology, 923-1292, Ishikawa, Japan

    Ryuhei Uehara

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© 2009 Springer-Verlag Berlin Heidelberg

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Saitoh, T., Yamanaka, K., Kiyomi, M., Uehara, R. (2009). Random Generation and Enumeration of Proper Interval Graphs. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-00202-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00201-4

  • Online ISBN: 978-3-642-00202-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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