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Workshop on Algorithms and Data Structures

WADS 1993: Algorithms and Data Structures pp 131–141Cite as

Connected domination and steiner set on asteroidal triple-free graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 709))

Abstract

An asteroidal triple is a set of three independent vertices such that between any two of them there exists a path that avoids the neighbourhood of the third. Graphs that do not contain an asteroidal triple are called asteroidal triple-free (AT-free) graphs. AT-free graphs strictly contain the well-known class of cocomparability graphs, and are not necessarily perfect. We present efficient polynomial-time algorithms for the minimum cardinality connected dominating set problem and the Steiner set problem on AT-free graphs. These results, in addition to solving these problems on this large class of graphs, also strengthen the conjecture of White. et. al. [9] that these two problems are algorithmically closely related.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, 600 036, Madras, India

    Hari Balakrishnan, Anand Rajaraman & C. Pandu Rangan

Authors
  1. Hari Balakrishnan
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  2. Anand Rajaraman
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  3. C. Pandu Rangan
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Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro Sue Whitesides

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© 1993 Springer-Verlag Berlin Heidelberg

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Balakrishnan, H., Rajaraman, A., Rangan, C.P. (1993). Connected domination and steiner set on asteroidal triple-free graphs. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_242

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  • DOI: https://doi.org/10.1007/3-540-57155-8_242

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57155-1

  • Online ISBN: 978-3-540-47918-5

  • eBook Packages: Springer Book Archive

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