  In this note, we analyze two random greedy processes on sparse random graphs
and hypergraphs with a given degree sequence. First we analyze the matching
process, which builds a set of disjoint edges one edge at a time; then we
analyze the independent process, which builds an independent set of vertices
one vertex at a time. We use the differential equations method and apply a
general theorem of Warnke. Our main contribution is to significantly reduce the
associated systems of differential equations and simplify the expression for
the final size of the matching or independent set.
