Consider a surface S and let M⊂S. If S∖M is not
connected, then we say M \emph{separates} S, and we refer to M as a
\emph{separating set} of S. If M separates S, and no proper subset of M
separates S, then we say M is a \emph{minimal separating set} of S. In
this paper we use methods of computational combinatorial topology to classify
the minimal separating sets of the orientable surfaces of genus g=2 and
g=3. The classification for genus 0 and 1 was done in earlier work, using
methods of algebraic topology.Comment: 24 pages, 5 figures, 2 tables (11 pages