Algorithmic problems in mobile computing environments

A mobile computer has become a powerful tool. From laptop computers to cellular phones, in the past decade mobile computers have become prevalent in society. In this thesis we shall review and present various algorithms for use with mobile computers; in particular algorithms for mobile ad hoc wireless networks.;Routing problems in ad hoc wireless networks have been one of the most intensely studied areas of research. We shall review various routing algorithms presented by others, verify some of their results, and present our own algorithms for a particular type of routing called fan routing, along with statistical analysis.;The frequency assignment problem has been investigated for many years. We shall investigate two frequency assignment problems for mobile networks. The first uses a limited amount of information to compute an assignment for a host when it is added to a network, where the remainder of the hosts have already been assigned frequencies. We shall present our algorithms and compare them. The second looks at particular graphs, known as outerplanar graphs, and how to use the minimal amount of frequencies for these graphs.;The final area we shall investigate is efficient update strategies for geometric computing with uncertainty. That is, if you know a property of some objects is true; after some time, is this property still true even if the objects have moved? We present a generalised algorithm for verifying any given property and use this generalised algorithm for the maximal points problem.