Greedy algorithms for tracking mobile users in ... - Semantic Scholar
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Greedy algorithms for tracking mobile users in ... - Semantic Scholar
When a call arrives, the user is searched for only in the vicinity of ... this work is to propose algorithms to optimally solve the reporting center problem for vicinity 2.
Discrete Applied Mathematics 121 (2002) 215–227
Greedy algorithms for tracking mobile users in special mobility graphs S. Olariua; ∗ , M.C. Pinottib , L. Wilsona a Department
b Department
of Computer Science, Old Dominion University, Norfolk, VA 23529-0162, USA of Mathematics, Laboratory of Computer Science and Telematics, University of Trento, I-38050 Povo (TN), Italy
Received 19 December 1998; received in revised form 8 January 2001; accepted 19 April 2001
Abstract 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 graphs. ? 2002 Elsevier Science B.V. All rights reserved. Keywords: Wireless networks; Interval graphs; Tracking problem
1. Introduction Wireless networks are designed to provide ubiquitous communication services to a large number of mobile users. For this, wireless networks of high capacity are required, whose implementation relies essentially on the infrastructure o:ered by existing cellular networks. A cellular network involves two distinct levels: a stationary level, consisting of
