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Efficient construction of a bounded-degree spanner with low weight

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Abstract

LetS be a set ofn points in ℝd and lett>1 be a real number. At-spanner forS is a graph having the points ofS as its vertices such that for any pairp, q of points there is a path between them of length at mostt times the Euclidean distance betweenp andq.

An efficient implementation of a greedy algorithm is given that constructs at-spanner having bounded degree such that the total length of all its edges is bounded byO (logn) times the length of a minimum spanning tree forS. The algorithm has running timeO (n logd n).

Applying recent results of Das, Narasimhan, and Salowe to thist-spanner gives anO(n logd n)-time algorithm for constructing at-spanner having bounded degree and whose total edge length is proportional to the length of a minimum spanning tree forS. Previously, noo(n 2)-time algorithms were known for constructing at-spanner of bounded degree.

In the final part of the paper, an application to the problem of distance enumeration is given.

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Authors and Affiliations

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

    S. Arya & M. Smid

Authors
  1. S. Arya
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  2. M. Smid
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Additional information

Communicated by K. Melhorn.

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

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Arya, S., Smid, M. Efficient construction of a bounded-degree spanner with low weight. Algorithmica 17, 33–54 (1997). https://doi.org/10.1007/BF02523237

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  • DOI: https://doi.org/10.1007/BF02523237

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