Geometric spanners for weighted point sets

M.A. Abam, M.T. Berg, de, M. Farshi, J. Gudmundsson, M.H.M. Smid

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)

Abstract

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 d w , where d w (p,q) is w(p)¿+¿d(p,q)¿+¿wq 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 d w -metric. For any given e>¿0, we can apply our method to obtain (5¿+¿e)-spanners with a linear number of edges for three cases: points in Euclidean space R d , points in spaces of bounded doubling dimension, and points on the boundary of a convex body in R d where d is the geodesic distance function. We also describe an alternative method that leads to (2¿+¿e)-spanners for points in R d and for points on the boundary of a convex body in R d . The number of edges in these spanners is O(nlogn). This bound on the stretch factor is nearly optimal: in any finite metric space and for any e>¿0, it is possible to assign weights to the elements such that any non-complete graph has stretch factor larger than 2¿-¿e.
Original languageEnglish
Pages (from-to)207-225
JournalAlgorithmica
Volume61
Issue number1
DOIs
Publication statusPublished - 2011

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