Dynamic range and frequency assignment problems (PDF)
More and more communication is nowadays performed using wireless networks: mobile phone telecommunication, robots or other devices that communicate via Bluetooth, and so on. The optimization of such wireless communication systems gives rise to many challenging algorithmic questions. Most problems studied in this thesis are inspired by this type of questions.
The first question we study is inspired by the problem of assigning frequencies to base stations in a mobile phone network. In the mobile phone telecommunication case, the locations of the base stations are given, together with the range within which they can serve customers. Since typically the ranges overlap, if a customer stands within the range of two different base stations that use the same frequency, then interference occurs and the customer cannot communicate with either of the two base stations. On the other end of the spectrum, if all base stations use a different frequency, the frequency range needed is large and hence costly or even not available at all. We therefore want to assign a frequency to each base station such that in any location within the range of at least one device, it is possible to communicate with at least one base station without suffering from interference.
The second problem is inspired by the problem of minimizing power consumption in wireless communication networks. Here one is given a collection of devices that can send information to other devices within their transmission range. A device can then communicate with another one via other devices, that is the devices form a communication network and a device can send a message to another one if there is a path from the former to the later device. To ensure connectivity between devices, it is obviously possible to have each device transmit to each other device by assigning large ranges. However this is not desirable as the power cost needed for such ranges can be too high, forcing, for instance, football robots to carry heavy batteries that would slow them down. On the other hand, if the ranges are too small, two robots might not be able to communicate with one another. We hence want an assignment of ranges that maintain a certain connectivity while minimising the energy cost.