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Repetition Detection in a Dynamic String
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Abstract:
A string UU for a non-empty string U is called a square. Squares have been well-studied both from a combinatorial and an algorithmic perspective. In this paper, we are the first to consider the problem of maintaining a representation of the squares in a dynamic string S of length at most n. We present an algorithm that updates this representation in n^o(1) time. This representation allows us to report a longest square-substring of S in O(1) time and all square-substrings of S in O(output) time. We achieve this by introducing a novel tool - maintaining prefix-suffix matches of two dynamic strings. We extend the above result to address the problem of maintaining a representation of all runs (maximal repetitions) of the string. Runs are known to capture the periodic structure of a string, and, as an application, we show that our representation of runs allows us to efficiently answer periodicity queries for substrings of a dynamic string. These queries have proven useful in static pattern matching problems and our techniques have the potential of offering solutions to these problems in a dynamic text setting.
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Keyword:
Data processing Computer science; dynamic algorithms; repetitions; runs; squares; string algorithms
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URN:
urn:nbn:de:0030-drops-111265
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URL: https://drops.dagstuhl.de/opus/volltexte/2019/11126/
https://doi.org/10.4230/LIPIcs.ESA.2019.5
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Sufficient Conditions for Efficient Indexing Under Different Matchings
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Amir, Amihood; Kondratovsky, Eitan. - : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2019. : LIPIcs - Leibniz International Proceedings in Informatics. 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019), 2019
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Sufficient Conditions for Efficient Indexing Under Different Matchings ...
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