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Space Lower Bounds for Online Pattern Matching

  • Raphaël Clifford
  • Markus Jalsenius
  • Ely Porat
  • Benjamin Sach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6661)

Abstract

We present space lower bounds for online pattern matching under a number of different distance measures. Given a pattern of length m and a text that arrives one character at a time, the online pattern matching problem is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. We require that the correct answer is given at each position with constant probability. We give Ω(m) bit space lower bounds for L 1, L 2, L  ∞ , Hamming, edit and swap distances as well as for any algorithm that computes the cross-correlation/convolution. We then show a dichotomy between distance functions that have wildcard-like properties and those that do not. In the former case which includes, as an example, pattern matching with character classes, we give Ω(m) bit space lower bounds. For other distance functions, we show that there exist space bounds of Ω(logm) and O(log2 m) bits. Finally we discuss space lower bounds for non-binary inputs and show how in some cases they can be improved.

Keywords

Hash Function Pattern Match Communication Complexity Edit Distance Character Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Raphaël Clifford
    • 1
  • Markus Jalsenius
    • 1
  • Ely Porat
    • 2
  • Benjamin Sach
    • 1
  1. 1.Dept. of Computer ScienceUniversity of BristolBristolUK
  2. 2.Dept. of Computer ScienceBar-Ilan UniversityRamat-GanIsrael

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