Approximation Algorithms for Directed Multi-Multiway Cut and Directed Multicut Problems

In this paper, we present approximation algorithms for the directed multi-multiway cut and directed multicut problems. The so called region growing paradigm [1] is modified and used for these two cut problems on directed graphs By this paradigm, we give for each problem an approximation algorithm such that both algorithms have an approximate factor. The work previously done on these problems need to solve k linear programming, whereas our algorithms require only one linear programming for obtaining a good approximate factor.