  We propose new filtering algorithms for the SEQUENCE constraint and some
extensions of the SEQUENCE constraint based on network flows. We enforce domain
consistency on the SEQUENCE constraint in $O(n^2)$ time down a branch of the
search tree. This improves upon the best existing domain consistency algorithm
by a factor of $O(\log n)$. The flows used in these algorithms are derived from
a linear program. Some of them differ from the flows used to propagate global
constraints like GCC since the domains of the variables are encoded as costs on
the edges rather than capacities. Such flows are efficient for maintaining
bounds consistency over large domains and may be useful for other global
constraints.
