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Space lower bounds for online pattern matching
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Clifford, Raphaël, Jalsenius, Markus, Porat, Ely and Sach, Ben (2013) Space lower bounds for online pattern matching. Theoretical Computer Science, 483 . pp. 68-74. doi:10.1016/j.tcs.2012.06.012 ISSN 0304-3975.
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Official URL: http://dx.doi.org/10.1016/j.tcs.2012.06.012
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 L1, L2, 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(log2m) bits. Finally we discuss space lower bounds for non-binary inputs and show how in some cases they can be improved.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Journal or Publication Title: | Theoretical Computer Science | ||||
Publisher: | Elsevier Science BV | ||||
ISSN: | 0304-3975 | ||||
Official Date: | 29 April 2013 | ||||
Dates: |
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Volume: | 483 | ||||
Page Range: | pp. 68-74 | ||||
DOI: | 10.1016/j.tcs.2012.06.012 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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