Time Space Optimal Algorithm for Computing Separators in Bounded Genus Graphs

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 $O(g^{1\mathrm{/}2}{n}^{1\mathrm{/}2}\log n)$-space to find an $O(g^{1\mathrm{/}2}{n}^{1\mathrm{/}2})$-sized separator of a graph having $n$ vertices and embedded on a surface of genus $g$.