Vertex Fault-Tolerant Spanners for Weighted Points in Polygonal Domains

Abstract

Given a set S of n points, a weight function w to associate a non-negative weight to each point in S, a positive integer k ≥ 1, and a real number ǫ > 0, we devise the following algorithms to compute a k-vertex fault-tolerant spanner network G(S, E) for the metric space induced by the weighted points in S: (1) When the points in S are located in a simple polygon, we present an algorithm to compute G with multiplicative stretch √ 10 + ǫ, and the number of edges in G (size of G) is O(kn(lg n) 2 ). ( 2) When the points in S are located in the free space of a polygonal domain P with h number of obstacles, we present an algorithm to compute G with multiplicative stretch 6 + ǫ and size O( √ hkn(lg n) 2 ). ( 3) When the points in S are located on a polyhedral terrain, we devise an algorithm to compute G with multiplicative stretch 6 + ǫ and size O(kn(lg n) 2 ).