Pattern matching in multiple streams

  • Authors:

  • Raphaël Clifford;Markus Jalsenius;Ely Porat;Benjamin Sach

  • Affiliations:

  • Department of Computer Science, University of Bristol, Bristol, UK;Department of Computer Science, University of Bristol, Bristol, UK;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel;Department of Computer Science, University of Warwick, Coventry, UK

  • Venue:
  • CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
  • Year:
  • 2012

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Abstract

We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match between a fixed pattern of length m and a newly updated stream. As is usual in the streaming context, the goal is to use as little space as possible while still reporting matches quickly. We give almost matching upper and lower space bounds for three distinct pattern matching problems. For exact matching we show that the problem can be solved in constant time per arriving symbol and O(m+s) words of space. For the k-mismatch and k-difference problems we give O(k) time solutions that require O(m+ks) words of space. In all three cases we also give space lower bounds which show our methods are optimal up to a single logarithmic factor. Finally we set out a number of open problems related to this new model for pattern matching.