The power of knowledge in linear search for an escaping target

Abstract

We consider linear search for an escaping target whose speed and/or initial distance from the origin may be unknown to the searcher. The 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. The oblivious mobile target that is moving away from the origin with a 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 four cases, depending on whether v and/or d is known to the searcher. The main contributions of this paper are new lower bounds as well as algorithms leading to new upper bounds for search in these settings. We present tight bounds for the cases when v is known. For the cases where v is unknown, we prove 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. These results solve an open problem proposed in Coleman et al. (2022) [11].