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Faster Dynamic Range Mode

Authors Bryce Sandlund, Yinzhan Xu

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ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Range Mode
  • Min-Plus Product

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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 Õ(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.

Cite As Get BibTex

Bryce Sandlund and Yinzhan Xu. Faster Dynamic Range Mode. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 94:1-94:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.94

Author Details

Bryce Sandlund
  • Cheriton School of Computer Science, University of Waterloo, Canada
Yinzhan Xu
  • CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA

Acknowledgements

We would like to thank Virginia Vassilevska Williams for her valuable comments on a draft of this paper. We would like to thank the anonymous reviewers for their helpful suggestions.

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