Improved approximation algorithms for Directed Steiner Forest

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...

Improved approximating 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 spanner problems and Directed Steiner Forest

We present an O( √ n log n)-approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices. A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, given a graph G = (V, E) with nonnegative edge lengths d : E → R≥0 and a stretch k ≥ 1, a subgraph H = (V, EH) is a k-spanner of G if ...

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