Some Pursuit-Evasion Problems on Grids

Dawes, R.W., Some pursuit-evasion problems on grids, Information Processing Letters 43 (1992) 241-247. In a rectangular grid, a pursuit-evation “game” is played according to simple rules. One player (the cop) wins if both players ever occupy either the same row or the same column of the grid. The other player (the robber) wins if the cop loses. Movement of the players is restricted to the rows and columns of the grid, and the speeds at which the players move are limited. We present a new upper bound for the minimum cop’s speed required to guarantee a win for the cop, and consider some variations on the problem.