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\U) or δ(U) is the set of edges of E linking all vertices of U to all vertices of V\U such that the induced subgraphs G[U] and G[V\U] are connected. Given a positive weight function w defined on E, the maximum connected sides cut problem is to find a connected sides cut Ω such that w(Ω) is maximum. This problem is NP-hard. In this paper, we give a linear time algorithm to solve the maximum connected sides cut problem 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.