  Significant advances in flow algorithms have changed the relative performance
of various approaches to algorithms for $L_p$ isotonic regression. We show a
simple plug-in method to systematically incorporate such advances, and advances
in determining violator dags, with no assumptions about the algorithms'
structures. The method is based on the standard algorithm for $L_0$ (Hamming
distance) isotonic regression (by finding anti-chains in a violator dag),
coupled with partitioning based on binary $L_1$ isotonic regression. For
several important classes of graphs the algorithms are already faster (in
O-notation) than previously published ones, close to or at the lower bound, and
significantly faster than those implemented in statistical packages. We
consider exact and approximate results for $L_p$ regressions, $p=0$ and $1 \leq
p < \infty$, and a variety of orderings.
