Tight Cell-Probe Bounds for Online Hamming Distance Computation

TL;DR

This paper establishes tight lower bounds for online Hamming distance computation in the cell-probe model, demonstrating the fundamental complexity limits of the problem with respect to input size and word length.

Contribution

It provides the first tight bounds for online Hamming distance computation in the cell-probe model, matching upper bounds and confirming the problem's inherent complexity.

Findings

Lower bound of Omega((d/w)*log n) per output

Bound holds under randomization and amortization

Bound is tight within the cell-probe model

Abstract

We show tight bounds for online Hamming distance computation in the cell-probe model with word size w. The task is to output the Hamming distance between a fixed string of length n and the last n symbols of a stream. We give a lower bound of Omega((d/w)*log n) time on average per output, where d is the number of bits needed to represent an input symbol. We argue that this bound is tight within the model. The lower bound holds under randomisation and amortisation.