Space lower bounds for online pattern matching

Authors:
Raphaël Clifford;Markus Jalsenius;Ely Porat;Benjamin Sach
Affiliations:
University of Bristol, Dept. of Computer Science, Bristol, UK;University of Bristol, Dept. of Computer Science, Bristol, UK;Bar-Ilan University, Dept. of Computer Science, Ramat-Gan, Israel;University of Bristol, Dept. of Computer Science, Bristol, UK
Venue:
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Year:
2011

Citing 11
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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(log m) 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.