This paper studies the online power cover problem on a line. Let \(\varvec{L}\) be a line and \(\varvec{S}\) be a set of sensors located on \(\varvec{L}\) , where each sensor can be assigned a power to generate a coverage area for serving users. The objective is to assign minimum powers to cover a sequence of users that arrive online on \(\varvec{L}\) . We first show a lower bound of \(\varvec{2}\) for this problem. Then, an online algorithm based on a greedy strategy is proposed, whose competitive ratio is at most \(\varvec{|S|}\) . Notably, this algorithm is the best possible online algorithm for the case \(\varvec{|S|=2}\) . Finally, we consider the special case with \(\varvec{S=\{s_0,s_1,s_2\}}\) and design an online algorithm whose competitive ratio depends on the distances between the sensors.
