  A common computational problem in multiple change-point models is to recover
the segmentations with $1$ to $K_{max}$ change-points of minimal cost with
respect to some loss function. Here we present an algorithm to prune the set of
candidate change-points which is based on a functional representation of the
cost of segmentations. We study the worst case complexity of the algorithm when
there is a unidimensional parameter per segment and demonstrate that it is at
worst equivalent to the complexity of the segment neighbourhood algorithm:
$\mathcal{O}(K_{max} n^2)$. For a particular loss function we demonstrate that
pruning is on average efficient even if there are no change-points in the
signal. Finally, we empirically study the performance of the algorithm in the
case of the quadratic loss and show that it is faster than the segment
neighbourhood algorithm.
