Triangle evacuation of 2 agents in the wireless model & the power of choosing a starting point

Abstract

The input to the Triangle Evacuation problem is a non-obtuse triangle ABC. A feasible solution is two unit-speed trajectories of mobile agents that start at some point on the perimeter and eventually visit every point on the perimeter of ABC. The goal is to find trajectories that minimize the evacuation cost, defined as the supremum, over all points T, of the time when T is first visited by one agent plus the distance from T to the other agent at that time. We introduce 4 different algorithmic problems arising by letting the starting edge and/or the starting point S on that edge to be chosen either by the algorithm or the adversary. To that end, we provide a tight analysis for the algorithm that has been proved to be optimal for the previously studied search domains, as well as we provide lower bounds for each of the problems.