Until now, two basic system models have been proposed for mobile computing. The “‘fixed backbone” mobile system model assumes two distinct sets of entities in a mobile network: a large number of mobile hosts, and relatively fewer, but more powerful, fixed hosts. All fixed hosts and the communication paths between them constitute the static or fixed network. The geographical area that is served by the fixed network is divided into smaller regions calIed cells. Each cell is served by a fixed host. A fixed host communicates with the mobile hosts within its cell via a wireless medium. On the other hand, the “ad-hoc” system model assumes that mobile hosts can form networks by using their own radio transmitters and receivers without participation of any fixed infrastructure. The structure of an ad-hoc mobile network is highly dynamic. In our work (see [3]) we deal with two fundamental problems of distributed computing, the problems of process or node counting and the leader election problem. In the case of mobile networks these problems preserve their importance, since they are building blocks for solution to more complicated problems (see [l]). We consider the case of both, mobile networks with fixed wired infrastructure and ad-hoc networks. In the first case we give an efficient protocol for counting the number of mobile hosts, that has a total cost of mCurrreless+O(n2)Cfised, where m and n are correspondingly the number of mobile hosts and the fixed nodes, and Cwireless and Gfi=ed are the costs of wireless and fixed network message exchange. Our protocol is based on the well known Echo algorithm and it moves successively most of the network activity on the static
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