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 > 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 1 0 + , and the number of edges in G (size of G) is O (k n (lg n) 2). (2) When the points in S are located in the free space of a polygonal domain with h number of obstacles, we present an algorithm to compute G with multiplicative stretch 6 + and size O (h k n (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 + and size O (k n (lg n) 2). [ABSTRACT FROM AUTHOR]