Top-k Color Queries on Tree Paths

We present O(n)-space data structures to support various range frequency queries on a given array A[0 : n − 1] or tree T with n nodes. Given a query consisting of an arbitrary pair of pre-order rank indices (i, j), our data structures return a least frequent element, mode, α-minority, or top-k colors (values) of the multiset of elements in the unique path with endpoints at indices i and j in A or T . We describe a data structure that supports range least frequent element queries on arrays in O( √ n/w) time, improving the Θ( √ n) worst-case time required by the data structure of Chan et al. (SWAT 2012), where w ∈ Ω(log n) is the word size in bits. We describe a data structure that supports path mode queries on trees in O(log log n √ n/w) time, improving the Θ( √ n log n) worst-case time required by the data structure of Krizanc et al. (ISAAC 2003). We describe the first data structures to support path least frequent 123 Algorithmica element queries, path α-minority queries, and path top-k color queries on trees in O(log log n √ n/w), O(α −1 log log n), and O(k) time, respectively, where α ∈ [0, 1] and k ∈ {1, . . . , n} are specified at query time.

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Linear-Space Data Structures for Range Frequency Queries on Arrays and Trees

Durocher

Shah

Skala

et al. 2014

Algorithmica

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Succinct Indices for Path Minimum, with Applications

Chan

Munro

et al. 2016

Algorithmica

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Data structures for categorical path counting queries

Kazi

2022

Theoretical Computer Science

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Top-k Color Queries on Tree Paths

Cited by 3 publications

References 18 publications

Linear-Space Data Structures for Range Frequency Queries on Arrays and Trees

Linear-Space Data Structures for Range Frequency Queries on Arrays and Trees

Succinct Indices for Path Minimum, with Applications

Data structures for categorical path counting queries

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