Sharif Digital Repository

A geometric network is an undirected weighted graph whose vertices are defined as points in a geometric space, such as the real d-dimensional space. The weight of each edge of the network is equal to the Euclidean distance between the two endpoints of that edge.Geometric networks are used to model many real systems such as roads, communication networks, etc. When designing a network, one may consider different criteria. For lots of applications, existence of a short path between any two points of the network is important. The direct connection between any two points of a network is the ideal lution; however, this not possible in many applications because of its high cost. In order to... 

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...