An Optimal Algorithm for Online Freeze-Tag

Josh Brunner, Julian Wellman, Ryuhei Uehara, Giuseppe Prencipe, Martin Farach-Colton
2020 Fun with Algorithms  
In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online variant of the problem, each frozen robot is not revealed until a specified time. Hammar, Nilsson, and Persson have shown that no online algorithm can achieve a competitive ratio better than 7/3 for online freeze-tag, and posed the question of
more » ... er an O(1)-competitive algorithm exists. We provide a (1+√2)-competitive algorithm for online time-dependent freeze-tag, and show that this is the best possible: there does not exist an algorithm which achieves a lower competitive ratio on every metric space.
doi:10.4230/ dblp:conf/fun/BrunnerW21 fatcat:o5jdnxua5rdrpchvfs7hpipqwu