Hamming Distance Oracle
Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus

TL;DR
This paper introduces data structures for efficiently computing Hamming distances between substrings of two strings, providing bounds and lower bounds for constant and general alphabets.
Contribution
It presents new data structures with specific time bounds for the Hamming distance oracle problem and establishes conditional lower bounds based on fast matrix multiplication.
Findings
Data structure with (nm/x) preprocess and O(x) query time for constant alphabet.
Data structure with (nm/) preprocess and O(x) query time for general alphabet.
Conditional lower bounds showing limits of data structure efficiency unless fast matrix multiplication is possible.
Abstract
In this paper, we present and study the \emph{Hamming distance oracle problem}. In this problem, the task is to preprocess two strings and of lengths and , respectively, to obtain a data-structure that is able to answer queries regarding the Hamming distance between a substring of and a substring of . For a constant size alphabet strings, we show that for every there is a data structure with preprocess time and query time. We also provide a combinatorial conditional lower bound, showing that for every and there is no data structure with query time and preprocess time unless combinatorial fast matrix multiplication is possible. For strings over general alphabet, we present a data structure with preprocess time and query time…
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Taxonomy
TopicsAdvanced Database Systems and Queries · Network Packet Processing and Optimization · Algorithms and Data Compression
