2021/12/23 by Amir, Amihood, Boneh, Itai
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.2112.12678
The Suffix Array SAS[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 SAS[i] in O(log5(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(log4(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.