Online searching/on the optimality of the geometric sequences for the m ray search – online searching

In a recent paper, we consider the following search problem: Given m concurrent branches (each a copy of R⁺), a searcher, initially placed at the origin, has to find an ‘exit’, which is at an unknown real distance d ≥ 1 > 0 from the origin on one of the m concurrent branches. The problem is to find a strategy that minimizes the worst-case ratio between the total distance traveled and the distance of the exit from the origin.