Geometric Spanners for Weighted Point Sets

Spanners of Additively Weighted Point Sets

We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p, r) where p is a point in the plane and r is a real number. The distance between two points (pi, ri) and (pj , rj) is defined as |pipj | − ri − rj . We show that in the case where all ri are positive numbers and |pipj | ≥ ri + rj for all i, j (in which case the po...

Fault-Tolerant Additive Weighted Geometric Spanners

Let S be a set of n points and let w be a function that assigns non-negative weights to points in S. The additive weighted distance dw(p, q) between two points p, q ∈ S is defined as w(p) + d(p, q) + w(q) if p 6= q and it is zero if p = q. Here, d(p, q) denotes the (geodesic) Euclidean distance between p and q. A graph G(S,E) is called a t-spanner for the additive weighted set S of points if fo...

Geometric Spanners

Geometric Spanners Name: Joachim Gudmundsson, Giri Narasimhan, Michiel Smid Affil./Addr. 1: School of Information Technologies, The University of Sydney, NSW, Australia Affil./Addr. 2: School of Computing & Information Sciences Florida International University, FL, USA Affil./Addr. 3: School of Computer Science Carleton University, ON, Canada

Spanners for Geometric Intersection Graphs

Efficient algorithms are presented for constructing spanners in geometric intersection graphs. For a unit ball graph in R, a (1+ǫ)-spanner with O(nǫ) edges is obtained using efficient partitioning of the space into hypercubes and solving bichromatic closest pair problems. The spanner construction has almost equivalent complexity to the construction of Euclidean minimum spanning trees. The resul...

A pseudo - metri for weighted point sets ?