Simple and Fast Rounding Algorithms for Directed and Node-weighted Multiway Cut

We study the multiway cut problem in directed graphs and one of its special cases, the node-weighted multiway cut problem in undirected graphs. In DIRECTED MULTIWAY CUT (DIR-MC) the input is an edge-weighted directed graph G = (V, E) and a set of k terminal nodes {s1, s2, . . . , sk} ⊆ V ; the goal is to find a min-weight subset of edges whose removal ensures that there is no path from si to sj for any i = j. In NODE-WEIGHTED MULTIWAY CUT (NODE-WT-MC) the input is a node-weighted undirected graph G and a set of k terminal nodes {s1, s2, . . . , sk} ⊆ V ; the goal is to find a min-weight subset of nodes whose removal ensures that there is no path from si to sj for any i = j. DIR-MC admits a 2-approximation [28] and NODE-WT-MC admits a 2(1 − 1 k )approximation [21], both via rounding of LP relaxations. Previous rounding algorithms for these problems, from nearly twenty years ago, are based on careful rounding of an optimum solution to an LP relaxation. This is particularly true ...

• Type: Journal
• Year: 2016
• Where: SODA
• Authors: Chandra Chekuri, Vivek Madan
• Keywords: Algorithms, SODA 2016