Distance-based location update and routing in irregular cellular networks

In this paper, we consider a class of cellular networks, called irregular cellular networks, which may have a non-uniform distribution of base stations and a non-uniform cell size. The communications (between base stations) graph of such a cellular network forms a so-called trigraph, i.e., a plane triangulation with inner vertices of degree at least six. We show that each trigraph with n vertices admits a labeling that assigns O(log² n) bit labels to vertices of the graph such that the distance between any two vertices u and v can be determined in constant time by merely inspecting the labels of u and v, without using any other information about the graph. Furthermore, we show that there is a labeling, assigning labels of size O(log² n) bits to vertices, which allows, given the label of a source vertex and the label of a destination, to compute in constant time the port number of the edge from the source that heads in the direction of the destination. These two results for trigraphs provide elegant solutions to a few problems in irregular cellular networks. The distance labeling scheme allows efficient implementation of the distance-based tracking protocol, by providing information, generally not available to the user, and means for accurate cell distance determination. Our routing and distance labeling schemes provide compact and efficient routing and connection re-routing protocols. Although these results are primarily developed for cellular networks, they may find applications also in other types of wireless networks that have a fixed backbone infrastructure.