Towards an $O(\sqrt[3]{\log n})$-Approximation Algorithm for {\sc Balanced Separator}

The c-Balanced Separator problem is a graph-partitioning problem in which given a graph G, one aims to find a cut of minimum size such that both the sides of the cut have at least cn vertices. In this paper, we present new directions of progress in the c-Balanced Separator problem. More specifically, we propose a new family of mathematical programs, which depends upon a parameter ǫ > 0, and extend the seminal work of Arora-Rao-Vazirani (ARV) [4] to show that the polynomial time solvability of the proposed family of programs implies an improvement in the approximation factor to O (