On Assessing the Performance of Randomized Algorithms

In this paper we study randomized algorithms with random input. We adapt to such algorithms the notion of probability of a false positive which is common in epidemiological studies. The probability of a false positive takes into account both the (controlled) error of the randomization and the randomness of the input, which needs to be modeled. We illustrate our idea on two classes of problems: primality testing and fingerprinting in strings transmission. Although in both cases the randomization has low error, in the first one the probability of a false positive is very low, while in the second one it is not. We end the paper with a discussion of randomness illustrated in a textbook example.