Addressing and Distances for Cellular Networks with Holes

There is still much research in the areas of routing and location updates in cellular communication networks. Given the limited amount of memory and power of these network devices it is desirable to find the most effective and resource conscious method for solving routing and location update problems. Recently, these problems have been addressed for simply connected cellular networks and significant results were achieved.  An effective method for addressing, location update and routing has been offered using a method of isometric embeddings into a set of three trees.  This method however does not fully work when a hole is present in the network.  To handle networks containing holes, a variation of the above method is required, where the cellular network will be decomposed into few sub-graphs that encompass the properties of the original network graph.  Proposed here is a method that will handle the above mentioned problems on cellular networks with holes, namely holes with disc structures and other shapes that have the convex property.  Also presented are two distinct methods for handling networks with multiple disc-structured holes.  These methods will also use sub-graphs to reduce the number of holes while preserving all shortest paths.