  We revisit the problem of searching for a target at an unknown location on a
line when given upper and lower bounds on the distance D that separates the
initial position of the searcher from the target. Prior to this work, only
asymptotic bounds were known for the optimal competitive ratio achievable by
any search strategy in the worst case. We present the first tight bounds on the
exact optimal competitive ratio achievable, parameterized in terms of the given
bounds on D, along with an optimal search strategy that achieves this
competitive ratio. We prove that this optimal strategy is unique. We
characterize the conditions under which an optimal strategy can be computed
exactly and, when it cannot, we explain how numerical methods can be used
efficiently. In addition, we answer several related open questions, including
the maximal reach problem, and we discuss how to generalize these results to m
rays, for any m >= 2.
