Near-real-time Solutions for Online String Problems

TL;DR

This paper introduces near-real-time online algorithms for classical string problems, improving worst-case update times to poly-log-logarithmic complexity using advanced suffix tree techniques.

Contribution

It develops the first online algorithms with worst-case poly-log-logarithmic update times for several string problems, surpassing previous amortized or poly-logarithmic bounds.

Findings

Achieved poly-log-logarithmic worst-case update time for string problems

Provided conversions between string data structures with sublinear space complexity

Enhanced online suffix tree-based algorithms for string processing

Abstract

Based on the Breslauer-Italiano online suffix tree construction algorithm (2013) with double logarithmic worst-case guarantees on the update time per letter, we develop near-real-time algorithms for several classical problems on strings, including the computation of the longest repeating suffix array, the (reversed) Lempel-Ziv 77 factorization, and the maintenance of minimal unique substrings, all in an online manner. Our solutions improve over the best known running times for these problems in terms of the worst-case time per letter, for which we achieve a poly-log-logarithmic time complexity, within a linear space. Best known results for these problems require a poly-logarithmic time complexity per letter or only provide amortized complexity bounds. As a result of independent interest, we give conversions between the longest previous factor array and the longest repeating suffix array in space and time bounds based on their irreducible representations, which can have sizes sublinear in the length of the input string.