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- W2865725787 abstract "Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an element at index $i$. For the range mode problem, our data structure supports all operations in $O(n^{2/3})$ deterministic time using only $O(n)$ space. This improves two results by Chan et al. cite{C14}: a linear space data structure supporting update and query operations in $tilde{O}(n^{3/4})$ time and an $O(n^{4/3})$ space data structure supporting update and query operations in $tilde{O}(n^{2/3})$ time. For the range least frequent problem, we address two variations. In the first, we are allowed to answer with an element of $A$ that may not appear in the query range, and in the second, the returned element must be present in the query range. For the first variation, we develop a data structure that supports queries in $tilde{O}(n^{2/3})$ time, updates in $O(n^{2/3})$ time, and occupies $O(n)$ space. For the second variation, we develop a Monte Carlo data structure that supports queries in $O(n^{2/3})$ time, updates in $tilde{O}(n^{2/3})$ time, and occupies $tilde{O}(n)$ space, but requires that updates are made independently of the results of previous queries. The Monte Carlo data structure is also capable of answering $k$-frequency queries; that is, the problem of finding an element of given frequency in the specified query range. Previously, no dynamic data structures were known for least frequent element or $k$-frequency queries." @default.
- W2865725787 created "2018-07-19" @default.
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- W2865725787 date "2018-07-10" @default.
- W2865725787 modified "2023-09-27" @default.
- W2865725787 title "Improved Time and Space Bounds for Dynamic Range Mode" @default.
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