The Tourist in the Shopping Arcade

A tourist is searching for a gift and moves along a shopping arcade until the desired object gets into sight. The location of the corresponding shop is not known in advance. Therefore in this on-line setting the tourist has to make a detour in comparison to an optimal off-line straight line path to the desired object. We can show that there is a strategy for the tourist, so that the path length is never greater than C∗ times the optimal off-line path length, where C∗ = 1.059401 . . . holds. Furthermore, there is no strategy that attains a competitive factor smaller than C∗.