2024/07/07 by Itai Boneh, Dvir Fried, Boneh, Itai +5
Computer Science · #Advanced Database Systems and Queries #Network Packet Processing and Optimization #Algorithms and Data Compression
paper · pdf · doi:10.48550/arxiv.2407.05430
In this paper, we present and study the Hamming distance oracle problem. In this problem, the task is to preprocess two strings S and T of lengths n and m, respectively, to obtain a data-structure that is able to answer queries regarding the Hamming distance between a substring of S and a substring of T. For a constant size alphabet strings, we show that for every x≤ nm there is a data structure with O(nm/x) preprocess time and O(x) query time. We also provide a combinatorial conditional lower bound, showing that for every ε > 0 and x ≤ nm there is no data structure with query time O(x) and preprocess time O(((nm)/(x))1-ε) unless combinatorial fast matrix multiplication is possible. For strings over general alphabet, we present a data structure with O(nm/√(x)) preprocess time and O(x) query time for every x ≤ nm.