  A graph separator is a subset of vertices of a graph whose removal divides
the graph into small components. Computing small graph separators for various
classes of graphs is an important computational task. In this paper, we present
a polynomial time algorithm that uses $O(g^{1/2}n^{1/2}\log n)$-space to find
an $O(g^{1/2}n^{1/2})$-sized separator of a graph having $n$ vertices and
embedded on a surface of genus $g$.
