Linear time algorithms for Clobber

Abstract

We prove that the single-player game clobber is solvable in linear time when played on a line or on a cycle. For this purpose, we show that this game is equivalent to an optimization problem on a set of words defined by seven classes of forbidden patterns. We also prove that, playing on the cycle, it is always possible to remove at least 2n/3 pawns, and we give a conformation for which it is not possible to do better, answering questions recently asked by Faria et al.