Faster Dynamic Range Mode

TL;DR

This paper introduces a deterministic data structure for dynamic range mode queries that operates faster than previous methods, achieving worst-case sublinear time per operation by combining advanced techniques.

Contribution

It presents a novel deterministic data structure that improves worst-case operation time for dynamic range mode queries, surpassing the $O(N^{2/3})$ barrier.

Findings

Achieves worst-case $ ilde{O}(N^{0.655994})$ time per operation.

Breaks the previous $O(N^{2/3})$ time barrier for dynamic range mode.

Combines ideas from Williams and Xu with a new Min-Plus product variant.

Abstract

In the dynamic range mode problem, we are given a sequence $a$ of length bounded by $N$ and asked to support element insertion, deletion, and queries for the most frequent element of a contiguous subsequence of $a$. In this work, we devise a deterministic data structure that handles each operation in worst-case $\tilde{O}(N^{0.655994})$ time, thus breaking the $O(N^{2/3})$ per-operation time barrier for this problem. The data structure is achieved by combining the ideas in Williams and Xu (SODA 2020) for batch range mode with a novel data structure variant of the Min-Plus product.