Searching in Euclidean Spaces with Predictions

We study the problem of searching for a target at some unknown location in $R^d$ 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 $p\in R^d$ that the searcher visits, we obtain a value $\lambda \left(p\right)$ such that $\left|pt\right|\le \lambda \left(p\right)\le c·\left|pt\right|$ , where $c\ge 1$ is a fixed constant, $t$ is the position of the target, and $\left|pt\right|$ is the Euclidean distance of p to $t$ . The cost of the search is the length of the path followed by the searcher. Our main positive result is a strategy that achieves $O\left(c^d\right)$ -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 $R^d$ , assuming that $c\ge 4$ .