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Collective Additive Tree Spanners of Homogeneously Orderable Graphs

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LATIN 2008: Theoretical Informatics (LATIN 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4957))

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Abstract

In this paper we investigate the (collective) tree spanners problem in homogeneously orderable graphs. This class of graphs was introduced by A. Brandstädt et al. to generalize the dually chordal graphs and the distance-hereditary graphs and to show that the Steiner tree problem can still be solved in polynomial time on this more general class of graphs. In this paper, we demonstrate that every n-vertex homogeneously orderable graph G admits

  • a spanning tree T such that, for any two vertices x,y of G, d T (x,y) ≤ d G (x,y) + 3 (i.e., an additive tree 3-spanner) and

  • a system of at most O(logn) spanning trees such that, for any two vertices x,y of G, a spanning tree exists with d T (x,y) ≤ d G (x,y) + 2 (i.e, a system of at most O(logn) collective additive tree 2-spanners).

These results generalize known results on tree spanners of dually chordal graphs and of distance-hereditary graphs. The results above are also complemented with some lower bounds which say that on some n-vertex homogeneously orderable graphs any system of collective additive tree 1-spanners must have at least Ω(n) spanning trees and there is no system of collective additive tree 2-spanners with constant number of trees.

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Authors and Affiliations

  1. Algorithmic Research Laboratory, Department of Computer Science, Kent State University, Kent, OH 44242, USA

    Feodor F. Dragan, Chenyu Yan & Yang Xiang

Authors
  1. Feodor F. Dragan
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  2. Chenyu Yan
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  3. Yang Xiang
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Editor information

Eduardo Sany Laber Claudson Bornstein Loana Tito Nogueira Luerbio Faria

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Dragan, F.F., Yan, C., Xiang, Y. (2008). Collective Additive Tree Spanners of Homogeneously Orderable Graphs. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_48

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  • DOI: https://doi.org/10.1007/978-3-540-78773-0_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78772-3

  • Online ISBN: 978-3-540-78773-0

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