use a principal pivoting algorithm to solve the linear complementarity
problem, and the combinatorics you get is an orientation of the n-
dimensional cube. Now, it's not an arbitrary orientation: The cube has
a unique sink. But not only that, even each face has a unique sink! So
it's desirable to be able to find the sink because finding the sink
also means finding the solution to the original problem. I will sketch
two algorithms which have both a deterministic and a randomised
version, and I will show some examples on which they are fast and
others on which they are slow. As it is work in progress, there are
likely to be more questions than answers...