TY - JOUR
T1 - Space lower bounds for online pattern matching
AU - Clifford, Raphaël
AU - Jalsenius, Markus
AU - Porat, Ely
AU - Sach, Benjamin
PY - 2013/4/29
Y1 - 2013/4/29
N2 - 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(log 2m) bits. Finally we discuss space lower bounds for non-binary inputs and show how in some cases they can be improved.
AB - 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(log 2m) bits. Finally we discuss space lower bounds for non-binary inputs and show how in some cases they can be improved.
UR - http://www.scopus.com/inward/record.url?scp=84876419455&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2012.06.012
DO - 10.1016/j.tcs.2012.06.012
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AN - SCOPUS:84876419455
SN - 0304-3975
VL - 483
SP - 68
EP - 74
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -