The Firing Squad Synchronization Problem for Two-Dimensional Arrays

We consider the firing squad synchronization problem for two-dimensional arrays. Any finite connected nonempty subset of the rectangular grid is permitted as an array. Any position in an array is permitted as a position of the general. We construct (1) solutions to this problem having minimal firing time for arrays in some classes of arrays and (2) (for each K) a solution to this problem having a “linear” firing time for any array having not more than K edges. We also show an example of string-type arrays (that is, lines of breadth 1 without loops (the position of the general is one of the ends)) of length N whose minimal firing time is less than 2N − 2.