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Efficient construction of a bounded degree spanner with low weight

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Algorithms — ESA '94 (ESA 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

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Abstract

Let S be a set of n points in ℝd and let t>1 be a real number. A t-spanner for S is a graph having the points of S as its vertices such that for any pair p, q of points there is a path between them of length at most t times the Euclidean distance between p and q. An efficient implementation of a greedy algorithm is given that constructs a t-spanner having bounded degree such that the total length of all its edges is bounded by O(log n) times the length of a minimum spanning tree for S. The algorithm has running time O(n logd n). Applying recent results of Das, Narasimhan and Salowe to this t-spanner gives an O(n logd n) time algorithm for constructing a t-spanner having bounded degree and whose total edge length is proportional to the length of a minimum spanning tree for S. Previously, no o(n 2) time algorithms were known for constructing a t-spanner of bounded degree. In the final part of the paper, an application to the problem of distance enumeration is given.

This work was supported by the ESPRIT Basic Research Actions Program, under contract No. 7141 (project ALCOM II).

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Sunil Arya & Michiel Smid

Authors
  1. Sunil Arya
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  2. Michiel Smid
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Arya, S., Smid, M. (1994). Efficient construction of a bounded degree spanner with low weight. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049396

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  • DOI: https://doi.org/10.1007/BFb0049396

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

  • eBook Packages: Springer Book Archive

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