  The alpha complex efficiently computes persistent homology of a point cloud
$X$ in Euclidean space when the dimension $d$ is low. Given a subset $A$ of
$X$, relative persistent homology can be computed as the persistent homology of
the relative \v{C}ech complex. But this is not computationally feasible for
larger point clouds. The aim of this note is to present a method for efficient
computation of relative persistent homology in low dimensional Euclidean space.
We introduce the relative Delaunay \v{C}ech complex whose homology is the
relative persistent homology. It can be constructed from the Delaunay complex
of an embedding of the point clouds in $(d+1)$-dimensional Euclidean space.
