Arithmetic Geographical Coding And Routing

In this thesis we study two research aspects of geographical routing: efficient geographical addressing and a new routing scheme. In the first part we offer a novel geographical routing algorithm that relies on a well known data structure called Quadtree. Quadtree is an efficient method of mapping a twodimensional area by recursively partitioning it to disjoint squares. We present a greedy, guaranteed delivery routing algorithm called Greedy-Quadtree-Greedy (GQG). The algorithm is robust to dynamics in the non-Quadtree edges and overcomes local minimums without the use of planarization, face routing, or searching. GQG is a tree-based routing algorithm; it makes greedy forwarding based on the location information that is extracted from the Quadtree addresses of the nodes. Bypassing voids is done by a concept of ”tree routing with shortcuts”, which can significantly improve hop stretch and load balancing. As part of the routing system, we present three algorithms: address distribution, network topology discovery, and geographical routing with guaranteed delivery. We keep all broadcasts bounded to one hop, and the nodes’ routing state depends on their degree rather than the overall network size. We prove the correctness of the algorithms and present simulations that show the protocol improvement over simple tree-based routing in load balancing and routing stretch. In the second part we present a bit efficient arithmetic geographical coding system that extends the coding system of Quadtree. Each codeword is a node’s geographical address and