$O(\log^2{k}/\log\log{k})$-Approximation Algorithm for Directed Steiner Tree: A Tight Quasi-Polynomial Time Algorithm

FasterDSP: A Faster Approximation Algorithm for Directed Steiner Tree Problem

Given a weighted directed graph G = (V, E, c), where c : E → R is an edge cost function, a subset X of vertices (terminals), and a root vertex vr, the directed Steiner tree problem (DSP) asks for a minimum-cost tree which spans the paths from root vertex vr to each terminal. Charikar et al.’s algorithm is well-known for this problem. It achieves an approximation guarantee of 1 ( 1) l l l k − in...

Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree

In the Steiner tree problem, we are given as input a connected n-vertex graph with edge weights in {1, 2, . . . ,W}, and a subset of k terminal vertices. Our task is to compute a minimum-weight tree that contains all the terminals. We give an algorithm for this problem with running time O(7.97 ·n · logW ) using O(n · lognW · log k) space. This is the first single-exponential time, polynomial-sp...

Quasi-polynomial Time Approximation Algorithm for Low-Degree Minimum-Cost Steiner Trees

A simple approximation algorithm for the internal Steiner minimum tree

For a metric graph G = (V,E) and R ⊂ V , the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning R such that every vertex in R is not a leaf. This note shows a simple polynomial-time 2ρapproximation algorithm, in which ρ is the approximation ratio for the Steiner minimum tree problem. The result improves the approximation ratio 2ρ+ 1 in [3].

A 1.376 Approximation Algorithm for the Steiner Tree Problem

The Steiner tree problem is one of the classic and most fundamental NP-hard problems: given an arbitrary weighted graph, seek a minimum-cost tree spanning a given subset of the vertices (terminals). This article presents a two-phase heuristic in greedy strategy that achieves an approximation ratio of ≈ 1.430 for general graphs. Through combining the two-phase heuristic and the LP-based approxim...