Faster Dynamic Range Mode
Bryce Sandlund, Yinzhan Xu

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 of length bounded by and asked to support element insertion, deletion, and queries for the most frequent element of a contiguous subsequence of . In this work, we devise a deterministic data structure that handles each operation in worst-case time, thus breaking the 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.
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Taxonomy
TopicsAlgorithms and Data Compression · Software Testing and Debugging Techniques · Machine Learning and Algorithms
