Deterministic knowledge about nearby nodes in a mobile one dimensional environment
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Mobile ad hoc networks consist of potentially moving, computing nodes that communicate via radio and do not have access to any fixed infrastructure. The knowl- edge about nearby nodes is a fundamental requirement and is part of many of the known solutions to problems in mobile and wireless networks including routing, broad- casting, distributed token circulation, etc. The existing solutions for this problem of knowing about neighbors are probabilistic. In this thesis, we give a first step towards a distributed, deterministic algorithm for finding out about the neighboring nodes. In particular, we focus on the problem of maintaining information about neighboring nodes in a one dimensional mobile and wireless ad hoc environment. Under some simplifying assumptions, we give an algorithm for the problem and a proof of correctness for the algorithm. We deal with efficiency in terms of both time and space. We prove a tight bound on the speed of propagation of the message when the nodes are sufficiently dense. We also consider the case when multiple clusters merge together. Our algorithm is space efficient in that the nodes do not include information about all the nodes they know in their broadcast message at all times. Nodes also store only the information about relevant nodes in their local store and purge information about nodes that have moved out of range. Our work shows that it is possible to solve the problem deterministically, and with reasonable values of the parameters, under some simplifying assumptions. Numerous interesting open questions remain in the area regarding how to relax the assumptions to make the approach more practical.