On properties of read and write sets in the Awerbuch-Peleg scheme for tracking mobile users

Abstract

An important issue in the design of a wireless network is the scheme used for tracking the locations of its mobile users. A formal scheme for efficient location tracking proposed by Awerbuch and Peleg uses a localitydpreserving distributed directory server whose construction is based on the graphdtheoretic notion of a regional matching. Although this scheme has been theoretically shown to have low worstdcase communication complexity, its implementation behavior is not known. We have implemented the Awerbuch–Peleg scheme in order to evaluate its performance and practicality. This paper, which stems from our implementation, examines properties of the read and write sets that are a key component of the hierarchical directories used in the scheme. We are particularly interested in read set size since it directly influences the scheme’s communication cost and performance. Our experimental results indicate that read set sizes in randomlydgenerated networks are much smaller than the theoretical bound. We derive some analytical results that help explain this behavior. In particular, we establish tight constant bounds for read set size in linear, grid and uniform degree balanced tree networks that are independent of the number of network nodes.