The online freeze-tag problem

Abstract

We consider the following problem from swarm robotics: given one or more "awake" robots in some metric space M, wake up a set of "asleep" robots. A robot awakens a sleeping robot by moving to the sleeping robot's position. When a robot awakens, it is available to assist in awakening other slumbering robots. We investigate offline and online versions of this problem and give a 2-competitive strategy and a lower bound of 2 in the case when M is discrete and the objective is to minimize the total movement cost. We also study the case when M is continuous and show a lower bound of 7/3 when the objective is to minimize the time when the last robot awakens. © Springer-Verlag Berlin Heidelberg 2006.