@inproceedings{f8de6b115d174187a637a82555a72a49,

title = "Geometric spanners for weighted point sets",

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.",

author = "M.A. Abam and {Berg, de}, M.T. and M. Farshi and J. Gudmundsson and M.H.M. Smid",

year = "2009",

doi = "10.1007/978-3-642-04128-0_17",

language = "English",

isbn = "978-3-642-04127-3",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "190--202",

editor = "A. Fiat and P. Sanders",

booktitle = "Algorithms - ESA 2009 (17th Annual European Symposium, Copenhagen, Denmark, September 7-9, 2009. Proceedings)",

address = "Germany",

}