Intuitive Analyses via Drift Theory
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Humans are bad with probabilities, and the analysis of randomized algorithms offers many pitfalls for the human mind. Drift theory is an intuitive tool for reasoning about random processes. It allows turning expected stepwise changes into expected first-hitting times. While drift theory is used extensively by the community studying randomized search heuristics, it has seen hardly any applications outside of this field, in spite of many research questions which can be formulated as first-hitting times. We state the most useful drift theorems and demonstrate their use for various randomized processes, including approximating vertex cover, the coupon collector process, a random sorting algorithm, and the Moran process. Finally, we consider processes without expected stepwise change and give a lemma based on drift theory applicable in such scenarios without drift. We use this tool for the analysis of the gambler's ruin process, for a coloring algorithm, for an algorithm for 2-SAT, and for a version of the Moran process without bias.
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