Jonas Lundgren

Thank you Jan for your comments. A faster version will soon be available.

Jan, thank you for the feedback. The compiler is the one that comes with Matlab 2010a. Sorry if that is a slow one. I rarely use MEX-code. I am fully satisfied if ichoose is five times slower than VChooseK.

Works very well and includes excellent documentation and examples

It looks like the algorithm unequally connects point vertically and horizontally.
Try this data, for example:
n = 1000;
k = 10;
x = linspace(0,1,n)';
y(:,1) = k*x + randn(n,1) - k/2;
y(:,2) = -k*x + randn(n,1) + k/2;
xx = [x;x];
yy = y(:);
alphavol([xx yy], 0.5, 1);