13.31 (1995)

Let $G$ be a permutation group on a set $\Omega$. A sequence of points of $\Omega$ is a base for $G$ if its pointwise stabilizer in $G$ is the identity. The greedy algorithm for a base chooses each point in the sequence from an orbit of maximum size of the stabilizer of its predecessors. Is it true that there is a universal constant $c$ with the property that, for any finite primitive permutation group, the greedy algorithm produces a base whose size is at most $c$ times the minimal base size?