Space lower bounds for online pattern matching
| Autor: | Benjamin Sach, Markus Jalsenius, Ely Porat, Raphaël Clifford |
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| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Discrete mathematics General Computer Science Hash function Distance measures Theoretical Computer Science Combinatorics Sliding window protocol Computer Science - Data Structures and Algorithms Data Structures and Algorithms (cs.DS) Edit distance Pattern matching Communication complexity Swap (computer programming) Hamming code Mathematics |
| Zdroj: | Theoretical Computer Science. 483:68-74 |
| ISSN: | 0304-3975 |
| DOI: | 10.1016/j.tcs.2012.06.012 |
| Popis: | 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 Omega(m) bit space lower bounds for L_1, L_2, L_\infty, 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 Omega(m) bit space lower bounds. For other distance functions, we show that there exist space bounds of Omega(log m) 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. Comment: 10 pages, 7 figures, CPM 2011 |
| Databáze: | OpenAIRE |
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