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Least Common Ancestor
Linear Time Algorithm
Suffix Array
Suffix Tree
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Computing Longest Common Substrings Via Suffix Arrays
Computing Longest Common Substrings Via Suffix Arrays,10.1007/9783540797098_10,Maxim A. Babenko,Tatiana A. Starikovskaya
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Computing Longest Common Substrings Via Suffix Arrays
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Maxim A. Babenko
,
Tatiana A. Starikovskaya
Given a set of N strings of
total length
n over alphabet Σ one may ask to find, for each 2 ≤ K ≤ N, the longest substring β that appears in at least K strings in A. It is known that this problem can be solved in O(n) time with the help of suffix trees. However, the resulting algorithm is rather complicated (in particular, it involves answering certain
least common ancestor
queries in O(1) time). Also, its running time and memory consumption may depend on . This paper presents an alternative, remarkably simple approach to the above problem, which relies on the notion of suffix arrays. Once the
suffix array
of some auxiliary O(n)length string is computed, one needs a simple O(n)time postprocessing to find the requested longest substring. Since a number of efficient and simple lineartime algorithms for constructing suffix arrays has been recently developed (with constant not depending on Σ), our approach seems to be quite practical.
Conference:
Computer Science Symposium in Russia  CSR
, pp. 6475, 2008
DOI:
10.1007/9783540797098_10
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