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.
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Notes
- 1.
For instance, Ben-Basat et al. write “We say that algorithm A is \(\epsilon \)-correct on a input instance S if it is able to approximate the number of 1’s in the last W bits, at every time instant while reading S, to within an additive error of \(W \epsilon \)”.
- 2.
Two events A and B are conditionally independent assuming event C if \(\Pr [A \wedge B \mid C] = \Pr [A \mid C] \cdot \Pr [B \mid C]\), which is equivalent to \(\Pr [A \mid B \wedge C] = \Pr [A \mid C]\).
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The first author has been supported by the DFG research project LO 748/13-1.
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Ganardi, M., Hucke, D., Lohrey, M. (2019). Derandomization for Sliding Window Algorithms with Strict Correctness. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_21
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