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arXiv · 1402.2712

Dynamic Partial Sorting

Jiamou Liu·Kostya Ross
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Abstract

The dynamic partial sorting problem asks for an algorithm that maintains lists of numbers under the link, cut and change value operations, and queries the sorted sequence of the $k$ least numbers in one of the lists. We first solve the problem in $O(k\log (n))$ time for queries and $O(\log (n))$ time for updates using the tournament tree data structure, where $n$ is the number of elements in the lists. We then introduce a layered tournament tree data structure and solve the same problem in $O(\log_φ^* (n) k\log (k))$ time for queries and $O\left(\log (n)\cdot\log^2\log (n)\right)$ for updates, where $φ$ is the golden ratio and $\log_φ^*(n)$ is the iterated logarithmic function with base $φ$.

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Jiamou Liu, Kostya Ross. 2014-04-18. Dynamic Partial Sorting. https://arxiv.org/abs/1402.2712

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