City Research Online

Abstract

We study the problem of searching for a target at some unknown location in Rd 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 ∈ Rd that the searcher visits, we obtain a value λ( p) such that | pt| ≤ λ( p) ≤ c · | pt|, where c ≥ 1 is a fixed constant, t is the position of the target, and | pt| 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(cd )-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 Rd , assuming that c ≥ 4.

Publication Type:	Article
Additional Information:	© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publisher Keywords:	Search games, Predictions, Distance, Computational geometry
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology School of Science & Technology > Department of Computer Science
SWORD Depositor:	Symplectic Administrator

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