Parameterized Approximation Algorithms for Bidirected Steiner Network Problems

Parameterized Approximation Algorithms for Directed Steiner Network Problems

Given an edge-weighted directed graph G = (V,E) and a set of k terminal pairs {(si, ti)}i=1, the objective of the Directed Steiner Network (DSN) problem is to compute the cheapest subgraph N of G such that there is an si → ti path in N for each i ∈ [k]. This problem is notoriously hard: there is no polytime O(2 1−ε )-approximation [Dodis & Khanna, STOC ’99], and it is W[1]-hard [Guo et al., SID...

Parameterized Algorithms for Stochastic Steiner Tree Problems

Since 1971, numerous parameterized algorithms for the Steiner tree problem have been published, first of which was introduced by Dreyfus and Wagner. However, up to today there is not a single parameterized algorithm for the two-stage stochastic Steiner tree problem. This problem is still practically important and deserves more attention. This document first presents an algorithm that has a wors...

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

Parameterized approximation algorithms for packing problems

In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing problem for which there is no known algorithm with approximation ratio α, and a parameter k. If the value of an optimal solution is at least k, we seek a soluti...