We develop and analyze algorithms for dispersing a swarm of primitive robots
in an unknown environment, R. The primary objective is to minimize the
makespan, that is, the time to fill the entire region. An environment is
composed of pixels that form a connected subset of the integer grid.
There is at most one robot per pixel and robots move horizontally or
vertically at unit speed. Robots enter R by means of k>=1 door pixels
Robots are primitive finite automata, only having local communication, local
sensors, and a constant-sized memory.
We first give algorithms for the single-door case (i.e., k=1), analyzing the
algorithms both theoretically and experimentally. We prove that our algorithms
have optimal makespan 2A-1, where A is the area of R.
We next give an algorithm for the multi-door case (k>1), based on a
wall-following version of the leader-follower strategy. We prove that our
strategy is O(log(k+1))-competitive, and that this bound is tight for our
strategy and other related strategies.Comment: 17 pages, 4 figures, Latex, to appear in Workshop on Algorithmic
Foundations of Robotics, 200