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arXiv · 2412.02828

Computing the Center of Uncertain Points on Cactus Graphs

Ran Hu·Divy H. Kanani·Jingru Zhang
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Abstract

In this paper, we consider the (weighted) one-center problem of uncertain points on a cactus graph. Given are a cactus graph $G$ and a set of $n$ uncertain points. Each uncertain point has $m$ possible locations on $G$ with probabilities and a non-negative weight. The (weighted) one-center problem aims to compute a point (the center) $x^*$ on $G$ to minimize the maximum (weighted) expected distance from $x^*$ to all uncertain points. No previous algorithm is known for this problem. In this paper, we propose an $O(|G| + mn\log mn)$-time algorithm for solving it. Since the input is $O(|G|+mn)$, our algorithm is almost optimal.

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Ran Hu, Divy H. Kanani, Jingru Zhang. 2024-12-03. Computing the Center of Uncertain Points on Cactus Graphs. https://arxiv.org/abs/2412.02828

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