Approximation Algorithms for Steiner and Directed Multicuts

Approximation Algorithms for Steiner and Directed Multicuts

In this paper we consider the steiner multicut problem. This is a generalization of the minimum multicut problem where instead of separating node pairs, the goal is to find a minimum weight set of edges that separates all given sets of nodes. A set is considered separated if it is not contained in a single connected component. We show an O(log3(kt)) approximation algorithm for the steiner multi...

Greedy approximation algorithms for directed multicuts

The Directed Multicut (DM) problem is: given a simple directed graph G = (V ,E) with positive capacities ue on the edges, and a set K ⊆ V × V of ordered pairs of nodes of G, find a minimum capacity K-multicut; C ⊆ E is a K-multicut if in G − C there is no (s, t)-path for any (s, t) ∈ K. In the uncapacitated case (UDM) the goal is to find a minimum size K-multicut. The best approximation ratio k...

Improved approximation algorithms for Directed Steiner Forest

We consider the k-Directed Steiner Forest (k-DSF) problem: Given a directed graph G = (V,E) with edge costs, a collection D ⊆ V × V of ordered node pairs, and an integer k ≤ |D|, find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are...

Approximation Algorithms for Directed Steiner Tree Problems

The Steiner tree problem which is known to be NP-Complete is the following. Given a weighted undirected graph G = (V;E), and a set X V of terminals, the objective is to nd a tree of minimum cost which connects all the terminals. If the graph is directed, in addition to X, we are given a root r 2 V , and the objective is to nd a minimum cost arborescence which connects the root to each of the te...

Approximation Algorithms for Directed Steiner Problems