A linear time algorithm for a variant of the max cut problem in series parallel graphs

Given a graph $G=(V, E)$, a connected sides cut $(U, V\backslash U)$ or $\delta (U)$ is the set of edges of E linking all vertices of U to all vertices of $V\backslash U$ such that the induced subgraphs $G[U]$ and $G[V\backslash U]$ are connected. Given a positive weight function $w$ defined on $E$, the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cut $\Omega$ such that $w(\Omega)$ is maximum. MAX CS CUT is NP-hard. In this paper, we give a linear time algorithm to solve MAX CS CUT for series parallel graphs. We deduce a linear time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.Comment: 6 page

Max-Cut and Max-Bisection are NP-hard on unit disk graphs

We prove that the Max-Cut and Max-Bisection problems are NP-hard on unit disk graphs. We also show that $\lambda$-precision graphs are planar for $\lambda$ > 1 / \sqrt{2}$

An approximation algorithm for the maximum cut problem and its experimental analysis

AbstractAn approximation algorithm for the maximum cut problem is designed and analyzed; its performance is experimentally compared with that of a neural algorithm and that of Goemans and Williamson's algorithm. Although the guaranteed quality of our algorithm in the worst-case analysis is poor, we give experimental evidence that its average behavior is better than that of Goemans and Williamson's algorithm