  We implement an algorithm RSHT (Random Simple-Homotopy) to study the
simple-homotopy types of simplicial complexes, with a particular focus on
contractible spaces and on finding substructures in higher-dimensional
complexes. The algorithm combines elementary simplicial collapses with pure
elementary expansions. For triangulated d-manifolds with d < 7, we show that
RSHT reduces to (random) bistellar flips.
  Among the many examples on which we test RSHT, we describe an explicit
15-vertex triangulation of the Abalone, and more generally, (14k+1)-vertex
triangulations of Bing's houses with k rooms, which all can be deformed to a
point using only six pure elementary expansions.
