# Vertex Fault-Tolerant Spanners for Weighted Points in Polygonal Domains

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 ϵ > 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)+ϵ, and the number of edges in G (size of G) is O(k n (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+ϵ and size O(√(h) k n(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+ϵ and size O(k n (n)^2).

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