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arXiv · 2412.02580

The Two-Center Problem of Uncertain Points on Trees

Haitao Xu·Jingru Zhang
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Abstract

In this paper, we consider the (weighted) two-center problem of uncertain points on a tree. Given are a tree $T$ and a set $\calP$ of $n$ (weighted) uncertain points each of which has $m$ possible locations on $T$ associated with probabilities. The goal is to compute two points on $T$, i.e., two centers with respect to $\calP$, so that the maximum (weighted) expected distance of $n$ uncertain points to their own expected closest center is minimized. This problem can be solved in $O(|T|+ n^{2}\log n\log mn + mn\log^2 mn \log n)$ time by the algorithm for the general $k$-center problem. In this paper, we give a more efficient and simple algorithm that solves this problem in $O(|T| + mn\log mn)$ time.

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Haitao Xu, Jingru Zhang. 2024-12-03. The Two-Center Problem of Uncertain Points on Trees. https://arxiv.org/abs/2412.02580

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