Linear Search for an Escaping Target with Unknown Speed

TL;DR

This paper investigates optimal search strategies for an autonomous agent seeking an escaping target with unknown speed and position, providing new bounds and algorithms that improve upon previous results and solve an open problem.

Contribution

It introduces new lower bounds and algorithms for linear search with an unknown target speed and position, achieving near-optimal competitive ratios and resolving an open problem.

Findings

Established a new lower bound for the search problem.

Developed algorithms with improved upper bounds.

Achieved near-optimal competitive ratios in the known distance case.

Abstract

We consider linear search for an escaping target whose speed and initial position are unknown to the searcher. A searcher (an autonomous mobile agent) is initially placed at the origin of the real line and can move with maximum speed $1$ in either direction along the line. An oblivious mobile target that is moving away from the origin with an unknown constant speed $v<1$ is initially placed by an adversary on the infinite line at distance $d$ from the origin in an unknown direction. We consider two cases, depending on whether $d$ is known or unknown. The main contribution of this paper is to prove a new lower bound and give algorithms leading to new upper bounds for search in these settings. This results in an optimal (up to lower order terms in the exponent) competitive ratio in the case where $d$ is known and improved upper and lower bounds for the case where $d$ is unknown. Our results solve an open problem proposed in [Coleman et al., Proc. OPODIS 2022].