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Constructing degree-3 spanners with other sparseness properties

  • Gautam Das
  • Paul J. Heffernan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 762)

Abstract

Let V be any set of n points in k-dimensional Euclidean space. A subgraph of the complete Euclidean graph is a t-spanner if for any u and v in V, the length of the shortest path from u to v in the spanner is at most t times d(u, v). We show that for any δ>1, there exists a polynomial-time constructible t-spanner (where t is a constant that depends only on δ and k) with the following properties. Its maximum degree is 3, it has at most n · δ edges, and its total edge weight is comparable to the minimum spanning tree of V (for k ≤ 3 its weight is O(1) · wt(MST), and for k>3 its weight is O(log n) · wt(MST)).

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Gautam Das
    • 1
  • Paul J. Heffernan
    • 1
  1. 1.Department of Mathematical SciencesMemphis State UniversityMemphis

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