  The alpha complex is a subset of the Delaunay triangulation and is often used
in computational geometry and topology. One of the main drawbacks of using the
alpha complex is that it is non-monotone, in the sense that if ${\cal
X}\subset{\cal X}'$ it is not necessarily (and generically not) the case that
the corresponding alpha complexes satisfy ${\cal A}_r({\cal X})\subset{\cal
A}_r({\cal X}')$. The lack of monotonicity may introduce significant
computational costs when using the alpha complex, and in some cases even render
it unusable. In this work we present a new construction based on the alpha
complex, that is homotopy equivalent to the alpha complex while maintaining
monotonicity. We provide the formal definitions and algorithms required to
construct this complex, and to compute its homology. In addition, we analyze
the size of this complex in order to argue that it is not significantly more
costly to use than the standard alpha complex.
