Algebraic Graph Theory - Nathan Benedetto Proenca

Title: A Primal-Dual Extension of the Goemans and Williamson Algorithm for Weighted Fractional Cut Cover

Abstract: A cut in a graph G = (V, E) is a set of edges which has one endpoint in S, for a given subset S of V. The fractional cut-covering number is the optimal value of a linear programming relaxation for the problem of covering each edge by a set of cuts. Beyond its role as part of Šámal's work on cut continuous functions, this graph parameter also arises as the gauge dual of the maximum cut problem. This connection allows one to extend the celebrated Goemans and Williamson approximation algorithm into this new setting, providing a deeper insight into both. This talk will survey some of the main points of this extension.