Randomisation in Online Algorithms, Load Balancing and other Dynamic Problems

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Computers are used to solve all kinds of problems emerging in the real world. Some of these problems are static. The computer is given some fixed input like a street map, the current location, and a destination. With these information it is, at least in principle, easy to calculate the fastest route to the destination.However, many problems are not static but dynamic. This is mostly due to the fact that we usually have no or very little information about future events like a sudden traffic jam on our pre-calculated route.A navigation system should be able to react to such unforeseeable events. The computation has to be ongoing and the solution has to be incessantly adjusted to the current situation and although previous decisions may turn out to be suboptimal, they cannot be reverted. Although it is impossible to avoid wrong decisions, the goal is to at least minimise the negative impact they have. The aim of this research is to give strategies to deal with problems that have some kind of dynamic aspect to them and study how randomisation can be used to obtain good solutions. The range of dynamic problems to be studied goes from concrete problems from practise to more abstract problems that emerge as sub-problems in numerous tasks.