Rheinische Friedrich - Wilhelms - Universität Bonn Institut für Informatik

A pride of lions are prowling among the vertices and edges of an n×n grid. If their paths are known in advance, is it possible to design a safe path for a man that avoids all lions, assuming that man and lion move at the same speed? In their recent paper [4], Dumitrescu et al. employed probabilistic arguments to show that O( √ n) lions can always be avoided. They raised the question if it is also possible to avoid O(n) lions. Using a proof technique quite different from theirs, we give a positive answer. Even bn 2 c lions can be avoided in dimension 2. However, there is no escaping from, by order of magnitude, Θ( d−1