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How to Use Spanning Trees to Navigate in Graphs

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Mathematical Foundations of Computer Science 2009 (MFCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5734))

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Abstract

In this paper, we investigate three strategies of how to use a spanning tree T of a graph G to navigate in G, i.e., to move from a current vertex x towards a destination vertex y via a path that is close to optimal. In each strategy, each vertex v has full knowledge of its neighborhood N G [v] in G (or, k-neighborhood D k (v,G), where k is a small integer) and uses a small piece of global information from spanning tree T (e.g., distance or ancestry information in T), available locally at v, to navigate in G. We investigate advantages and limitations of these strategies on particular families of graphs such as graphs with locally connected spanning trees, graphs with bounded length of largest induced cycle, graphs with bounded tree-length, graphs with bounded hyperbolicity. For most of these families of graphs, the ancestry information from a BFS-tree guarantees short enough routing paths. In many cases, the obtained results are optimal up to a constant factor.

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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 & Yang Xiang

Authors
  1. Feodor F. Dragan
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  2. Yang Xiang
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Editors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Research partially funded by grant APVV 0433-06, Bratislava, Slovakia

    Rastislav Královič

  2. Members of EACSL Jury for the Ackermann Award, Poland

    Damian Niwiński

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Dragan, F.F., Xiang, Y. (2009). How to Use Spanning Trees to Navigate in Graphs. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_25

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  • DOI: https://doi.org/10.1007/978-3-642-03816-7_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03815-0

  • Online ISBN: 978-3-642-03816-7

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