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ESA
2009
Springer

Geometric Spanners for Weighted Point Sets

14 years 4 months ago
Geometric Spanners for Weighted Point Sets
Let (S, d) be a finite metric space, where each element p ∈ S has a non-negative weight w(p). We study spanners for the set S with respect to weighted distance function dw, where dw(p, q) is w(p) + d(p, q) + w(q) if p = q and 0 otherwise. We present a general method for turning spanners with respect to the d-metric into spanners with respect to the dw-metric. For any given ε > 0, we can apply our method to obtain (5 + ε)-spanners with a linear number of edges for three cases: points in Euclidean space Rd , points in spaces of bounded doubling dimension, and points on the boundary of a convex body in Rd where d is the geodesic distance function. We also describe an alternative method that leads to (2 + ε)-spanners for points in Rd and for points on the boundary of a convex body in Rd . The number of edges in these spanners is O(n log n). This bound on the stretch factor is nearly optimal: in any finite metric space and for any ε > 0, it is possible to assign weights to the...
Mohammad Ali Abam, Mark de Berg, Mohammad Farshi,
Added 24 Jul 2010
Updated 24 Jul 2010
Type Conference
Year 2009
Where ESA
Authors Mohammad Ali Abam, Mark de Berg, Mohammad Farshi, Joachim Gudmundsson, Michiel H. M. Smid
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