Periodicity in Data Streams with Wildcards
Funda Erg\"un, Elena Grigorescu, Erfan Sadeqi Azer, Samson Zhou

TL;DR
This paper introduces algorithms for detecting periodic patterns in data streams with wildcards, providing a two-pass method with sublinear space and a one-pass randomized approach for specific cases, advancing streaming pattern detection.
Contribution
The paper presents the first two-pass and one-pass streaming algorithms for wildcard-period detection, with space complexity bounds and conditions for their applicability.
Findings
Two-pass algorithm computes wildcard-periods with $ ilde{O}(k^3)$ space.
One-pass randomized algorithm finds certain wildcard-periods efficiently.
Problem cannot be solved in sublinear space in one pass for general cases.
Abstract
We investigate the problem of detecting periodic trends within a string of length , arriving in the streaming model, containing at most wildcard characters, where . A wildcard character is a special character that can be assigned any other character. We say has wildcard-period if there exists an assignment to each of the wildcard characters so that in the resulting stream the length prefix equals the length suffix. We present a two-pass streaming algorithm that computes wildcard-periods of using bits of space, while we also show that this problem cannot be solved in sublinear space in one pass. We then give a one-pass randomized streaming algorithm that computes all wildcard-periods of with and no wildcard characters appearing in the last symbols of , using…
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Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · DNA and Biological Computing
