Computing the Center of Uncertain Points on Cactus Graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912143348072448 |
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| author | Hu, Ran Kanani, Divy H. Zhang, Jingru |
| author_facet | Hu, Ran Kanani, Divy H. Zhang, Jingru |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_02828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing the Center of Uncertain Points on Cactus Graphs Hu, Ran Kanani, Divy H. Zhang, Jingru Data Structures and Algorithms 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. |
| title | Computing the Center of Uncertain Points on Cactus Graphs |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2412.02828 |