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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.04964 |
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Table of Contents:
- We study the problem of searching for a target at some unknown location in $\mathbb{R}^d$ when additional information regarding the position of the target is available in the form of predictions. In our setting, predictions come as approximate distances to the target: for each point $p\in \mathbb{R}^d$ that the searcher visits, we obtain a value $λ(p)$ such that $|p\bm{t}|\le λ(p) \le c\cdot |p\bm{t}|$, where $c\ge 1$ is a fixed constant, $\bm{t}$ is the position of the target, and $|p\bm{t}|$ is the Euclidean distance of $p$ to $\bm{t}$. The cost of the search is the length of the path followed by the searcher. Our main positive result is a strategy that achieves $(10c)^{d+1}$-competitive ratio, even when the constant $c$ is unknown. We also give a lower bound of roughly $(c/4)^{d-1}$ on the competitive ratio of any search strategy in $\RR^d$, assuming that $c\ge 4$.