文章基本信息

标题：Searching Long Repeats in Streams
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作者：Oleg Merkurev ; Arseny M. Shur
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：128
页码：1-14
DOI：10.4230/LIPIcs.CPM.2019.31
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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}).
关键词：Longest repeated substring; longest repeated reversed substring; streaming algorithm; Karp; Rabin fingerprint; suffix tree