A perimeter–time CA for the queen bee problem

Algorithms for Leader Election by Cellular Automata

“…This paper explains in a more detailed manner the results presented in [6] and [8], namely solutions to this problem in three different frameworks, all on Euclidean lattices We have to mention that Beckers and Worsch simultaneously and independently presented a similar solution in [2], for perimeters of figures in 2 , also in linear time. In arbitrary dimensions, the problem is much more difficult, and the best solution we knew of before this paper was the one in [3].…”

“…The leader will be one such square. At the same time, we also consider the dual graph, composed of the edges and corners of these squares, which is isomorphic to 2 . We continue to call cells squares, to which we associate the FSA, as usual as explained in the Introduction.…”

“…Compared to [2] and to [6], that is, to the algorithms discussed above, this solution can be slower, since it is quadratic in the eccentricity, while the previous ones are linear in the surface, which can be linear in the eccentricity. However, the important advantage of this last algorithm is the extension to any connected figures in any dimension.…”