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 [Formula: see text], and a real number [Formula: see text], we devise the following algorithms to compute a k-vertex fault-tolerant spanner network [Formula: see text] 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 [Formula: see text], and the number of edges in G (size of G) is [Formula: see text]. (2) When the points in S are located in the free space of a polygonal domain [Formula: see text] with h number of obstacles, we present an algorithm to compute G with multiplicative stretch [Formula: see text] and size [Formula: see text]. (3) When the points in S are located on a polyhedral terrain, we devise an algorithm to compute G with multiplicative stretch [Formula: see text] and size [Formula: see text].