References & Citations
Computer Science > Discrete Mathematics
Title: Linear Search for an Escaping Target with Unknown Speed
(Submitted on 22 Apr 2024 (v1), last revised 23 Apr 2024 (this version, v2))
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].
Submission history
From: Jared Coleman [view email][v1] Mon, 22 Apr 2024 16:00:24 GMT (37kb)
[v2] Tue, 23 Apr 2024 14:42:48 GMT (37kb)
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