Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2019.31
URN: urn:nbn:de:0030-drops-105029
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10502/
Merkurev, Oleg ; Shur, Arseny M.
Searching Long Repeats in Streams
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Abstract
We consider two well-known related problems: Longest Repeated Substring (LRS) and Longest Repeated Reversed Substring (LRRS). Their streaming versions cannot be solved exactly; we show that only approximate solutions by Monte Carlo algorithms are possible, and prove a lower bound on consumed memory. For both problems, we present purely linear-time Monte Carlo algorithms working in O(E + n/E) space, where E is the additive approximation error. Within the same space bounds, we then present nearly real-time solutions, which require O(log n) time per symbol and O(n + n/E log n) time overall. The working space exactly matches the lower bound whenever E=O(n^{0.5}) and the size of the alphabet is Omega(n^{0.01}).
BibTeX - Entry
@InProceedings{merkurev_et_al:LIPIcs:2019:10502,
author = {Oleg Merkurev and Arseny M. Shur},
title = {{Searching Long Repeats in Streams}},
booktitle = {30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
pages = {31:1--31:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-103-0},
ISSN = {1868-8969},
year = {2019},
volume = {128},
editor = {Nadia Pisanti and Solon P. Pissis},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10502},
URN = {urn:nbn:de:0030-drops-105029},
doi = {10.4230/LIPIcs.CPM.2019.31},
annote = {Keywords: Longest repeated substring, longest repeated reversed substring, streaming algorithm, Karp, Rabin fingerprint, suffix tree}
}
| Keywords: | Longest repeated substring, longest repeated reversed substring, streaming algorithm, Karp, Rabin fingerprint, suffix tree | |
| Seminar: | 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 06.06.2019 |
