Sharif Digital Repository

A geometric network on a set V of points in d-dimensional Euclidean space is a weighted undirected graph G(V,E) with vertex set V such that the weight of an edge is the Euclidean distance between its endpoints. We say that the geometric network G(V,E) is a t-spanner of V, for a t > 1, if for each pair of points u and v in V there exists a path in G between u and v of length at most t times the Euclidean distance between u and v. In this thesis, we introduce the new concept of local t-spanners and present some algorithms to construct these geometric graphs. Suppose Gc(V ) is a complete graph and F is a family of convex regions, for instance set of half planes, squares and circles. The graph...