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

TL;DR

This paper introduces improved approximation algorithms for directed multi-multiway cut and multicut problems that reduce the number of linear programs needed, enhancing efficiency while maintaining the same approximation factor.

Contribution

The paper presents novel approximation algorithms that use a modified region growing paradigm, requiring only one linear program instead of multiple, thus improving computational efficiency.

Findings

Approximation factor of O(k) achieved for both problems.

Algorithms require only one linear programming problem.

Enhanced running time compared to previous methods.

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.