Parameterized Matching in the Streaming Model

Authors Markus Jalsenius, Benny Porat, Benjamin Sach

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Markus Jalsenius
Benny Porat
Benjamin Sach

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Markus Jalsenius, Benny Porat, and Benjamin Sach. Parameterized Matching in the Streaming Model. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 400-411, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


We study the problem of parameterized matching in a stream where we want to output matches between a pattern of length m and the last m symbols of the stream before the next symbol arrives. Parameterized matching is a natural generalisation of exact matching where an arbitrary one-to-one relabelling of pattern symbols is allowed. We show how this problem can be solved in constant time per arriving stream symbol and sublinear, near optimal space with high probability. Our results are surprising and important: it has been shown that almost no streaming pattern matching problems can be solved (not even randomised) in less than Theta(m) space, with exact matching as the only known problem to have a sublinear, near optimal space solution. Here we demonstrate that a similar sublinear, near optimal space solution is achievable for an even more challenging problem.
  • Pattern matching
  • streaming algorithms
  • randomized algorithms


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