An approximation algorithm to the k-Steiner Forest problem

A Primal-Dual Approximation Algorithm for the Steiner Forest Problem

Given an undirected graph with nonnegative edge-costs, a subset of nodes of size k called the terminals, and an integer q between 1 and k, the minimum q-Steiner forest problem is to find a forest of minimum cost with at most q trees that spans all the terminals. When q = 1, we have the classical minimum-cost Steiner tree problem on networks. We adapt a primal-dual approximation algorithm for th...

An Approximation Algorithm for the Euclidean Bottleneck Steiner Tree Problem

Given two sets of points in the plane, P of n terminals and S of m Steiner points, a Steiner tree of P is a tree spanning all points of P and some (or none or all) points of S. A Steiner tree with length of longest edge minimized is called a bottleneck Steiner tree. In this paper, we study the Euclidean bottleneck Steiner tree problem: given two sets, P and S, and a positive integer k ≤ m, find...

An Approximation Algorithm for the Euclidean Bottleneck Steiner Tree Problem

Given two sets of points in the plane, P of n terminals and S of m Steiner points, a Steiner tree of P is a tree spanning all points of P and some (or none or all) points of S. A Steiner tree with length of longest edge minimized is called a bottleneck Steiner tree. In this paper, we study the Euclidean bottleneck Steiner tree problem: given two sets, P and S, and a positive integer k ≤ m, find...

An Approximation Algorithm for the Covering Steiner Problem

An approximation algorithm for a bottleneck k-Steiner tree problem in the Euclidean plane

We study a bottleneck Steiner tree problem: given a set P = {p1,p2, . . . , pn} of n terminals in the Euclidean plane and a positive integer k, find a Steiner tree with at most k Steiner points such that the length of the longest edges in the tree is minimized. The problem has applications in the design of wireless communication networks. We give a ratio-1.866 approximation algorithm for the pr...