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

Abstract

In this paper, we present two approximation algorithms for the directed multi-multiway cut and directed multicut problems. The so called region growing paradigm \cite{1} is modified and used for these two cut problems on directed graphs. By using this paradigm, we give for each problem an approximation algorithm such that both algorithms have the approximate factor $O(k)$ the same as the previous works done on these problems. However, the previous works need to solve $k$ linear programming, whereas our algorithms require only one linear programming. Therefore, our algorithms improve the running time of the previous algorithms.

arXiv commentThis version is completely correct and does not have any problem. All mistakes are corrected in this version. AUT Journal of Mathematics and Computing (2020)