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Faster Linear-Space Data Structures for Path Frequency Queries

Author Ovidiu Rața

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Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
Keywords
  • Data structure
  • Range query
  • Mode
  • Minority
  • Least frequent element
  • Trees
  • Linear-space
  • Path query

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Abstract

We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path α-minority queries. We present the first linear-space data structures, requiring O(n √{nw}) preprocessing time, that can answer path mode and path least frequent element queries in O(√{n/w}) time. This improves upon the best previously known bound of O(log log n √{n/w}) achieved by Durocher et al. [Durocher et al., 2016] in 2016. 
For the path α-minority problem, where α is specified at query time, we reduce the query time of the linear-space data structure of Durocher et al. [Durocher et al., 2016] from O(α^{-1}log log n) down to O(α^{-1}) by employing a simple randomized algorithm with a success probability ≥ 1/2. 
We also present the first linear-space data structure supporting "Path Maximum g-value Color" queries in O(√{n/w}) time, requiring O(n √{nw}) preprocessing time. This general framework encapsulates both path mode and path least frequent element queries. For our data structures, we consider the word-RAM model with w ∈ Ω(log n), where w is the word size in bits.

Cite As Get BibTex

Ovidiu Rața. Faster Linear-Space Data Structures for Path Frequency Queries. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.37

Author Details

Ovidiu Rața
  • University of Copenhagen, Denmark

Funding

Supported by VILLUM Foundation grant 54451, Basic Algorithms Research Copenhagen (BARC).

Acknowledgements

I wish to thank Professor Mikkel Thorup for his valuable support as my Master’s Thesis supervisor. I also wish to thank the anonymous reviewers of SWAT 2026 for their meaningful feedback, which helped improve the paper.

References

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