Reporting Center Problem for Interval Graphs and Trees

Abstract In this thesis we have studied the reporting center problem for interval graphs and trees. The reporting center strategy is one of many strategies used to track the mobile users of a wireless network. The reporting center problem arises from the need to improve the efficiency, which is accomplished by balancing the cost of searching for a user against the cost of location-reporting by a user. In the reporting center strategy, a subset of the base stations of the cellular network is selected as reporting centers, to which mobile users report their locations when visiting their cells. The set of non-reporting centers associated with a reporting center is called its vicinity. To route an incoming call, the network locates a user by searching in the vicinity of the last contacted reporting center. The size of the vicinity of a reporting center determines the searching and updating cost of the cellular network. It is thus an objective to minimize the number of reporting centers subject to the constraint that the size of the vicinity of each reporting center is bounded by a constant Z> 0. The problem has been shown to be NP-complete for arbitrary graphs for Z ≥ 2. The major contribution of this work is divided into two parts: (1) an algorithm that solves the reporting center problem for arbitrary vicinity for interval graphs, thereby improving a previous result which only solves for vicinity Z = 2 for interval graphs and for arbitrary vicinity for proper interval graphs, and (2) an O(n) time algorithm that solves the reporting center problem for trees, which is better than the previous O(nZ , )r esult. ii Acknowledgement