Derandomization for Sliding Window Algorithms with Strict Correctness∗

Abstract

In the sliding window streaming model the goal is to compute an output value that only depends on the last n symbols from the data stream. Thereby, only space sublinear in the window size n should be used. Quite often randomization is used in order to achieve this goal. In the literature, one finds two different correctness criteria for randomized sliding window algorithms: (i) one can require that for every data stream and every time instant t, the algorithm computes a correct output value with high probability, or (ii) one can require that for every data stream the probability that the algorithm computes at every time instant a correct output value is high. Condition (ii) is stronger than (i) and is called "strict correctness" in this paper. The main result of this paper states that every strictly correct randomized sliding window algorithm can be derandomized without increasing the worst-case space consumption.

Sliding Window Algorithms for Regular Languages

“…A randomized sliding window algorithm that fulfills the latter (stronger) correctness criterion is called strictly correct in [45]. This model is for instance implicitly used in [13,26].…”

“…This model is for instance implicitly used in [13,26]. In [45] it is shown that every strictly correct randomized sliding window algorithm can be derandomized without increasing the space complexity. This result is shown in a very general context for arbitrary approximation problems.…”