On the complexity of location management in wireless networks

A fundamental issue in wireless networking is the design of efficient strategies for locating mobile users. In order to locate a mobile user, the network may page the user in each possible location in a paging area. To reduce the paging cost, a mobile user may periodically update its current location to the network. There is an obvious tradeoff between the paging and updating costs; increasing one cost leads to the decrease in the other one. A location management algorithm specifies the paging and updating strategies. We study the worst case performance of location management algorithms in networks whose configurations can be modeled by regular graphs. We derive tight lower bounds on the cost function C(m), defined as a convex combination of the number of updates and the maximum size of the paging area, in terms of the number of moves m made by a mobile user. Moreover, the upper bounds on C(m) for a variety of location management strategies are considered. We show that a movement-based algorithm is nearly optimal in terms of the cost C(m). The results are derived for regular graphs of degree two and of degree six, and can be easily extended to other regular graphs using our techniques.