  In this paper we study algorithms for tiling problems. We show that the
conditions $(T1)$ and $(T2)$ of Coven and Meyerowitz, conjectured to be
necessary and sufficient for a finite set $A$ to tile the integers, can be
checked in time polynomial in ${diam}(A)$. We also give heuristic algorithms to
find all non-periodic tilings of a cyclic group $Z_N$. In particular we carry
out a full classification of all non-periodic tilings of $Z_{144}$.
