Dynamic Suffix Array with Sub-linear update time and Poly-logarithmic Lookup Time
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The Suffix Array SA_S[1… n] of an n-length string S is a lexicographically sorted array of the suffixes of S. The suffix array is one of the most well known and widely used data structures in string algorithms. We present a data structure for maintaining a representation of the suffix array of a dynamic string which undergoes symbol substitutions, deletions, and insertions. For every string manipulation, our data structure can be updated in O(n^2/3) time (ignoring multiplicative polylogarithmic factors) with n being the current length of the string. For an input query i∈ [1… n], our data structure reports SA_S[i] in O(log^5(n)) time. We also present a faster data structure, with O(√(n)) update time (ignoring multiplicative polylogarithmic factors), for maintaining the Inverted Suffix Array of a dynamic string undergoing symbol substitutions updates. For an input query i∈ [1… n], our data structure reports the i'th entry in the inverted suffix array in O(log^4(n)) time. Our data structures can be used to obtain sub-linear dynamic algorithms for several classical string problems for which efficient dynamic solutions were not previously known.
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