Greedy algorithms for tracking mobile users in special mobility graphs

An important issue in wireless networks is the design and analysis of strategies for tracking mobile users. Several strategies have been proposed that aim at balancing the cost of updating the user position and the cost of locating a mobile user. The recently proposed reporting center strategy partitions the cellular network into reporting and non-reporting cells, and associates with each reporting cell a set of non-reporting cells, called its vicinity. The users report their position only when they visit a reporting cell. When a call arrives, the user is searched for only in the vicinity of the last visited reporting center. For a given constant "Z", the reporting center problem asks for a set of reporting cells of minimum cardinality such that each selected cell has a vicinity of size at most "Z" so that the update cost is minimized and the locating cost is bounded by "Z". The problem was shown to be "NP"-hard for arbitrary graphs and "Z>=2". The main contribution of this work is to propose algorithms to optimally solve the reporting center problem for vicinity 2 on interval graphs and for arbitrary vicinity on proper interval graph.