TY - GEN
T1 - Space lower bounds for online pattern matching
AU - Clifford, Raphaël
AU - Jalsenius, Markus
AU - Porat, Ely
AU - Sach, Benjamin
PY - 2011
Y1 - 2011
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 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(log 2 m) 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 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(log 2 m) 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=79960079143&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-21458-5_17
DO - 10.1007/978-3-642-21458-5_17
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AN - SCOPUS:79960079143
SN - 9783642214578
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 184
EP - 196
BT - Combinatorial Pattern Matching - 22nd Annual Symposium, CPM 2011, Proceedings
T2 - 22nd Annual Symposium on Combinatorial Pattern Matching, CPM 2011
Y2 - 27 June 2011 through 29 June 2011
ER -