距离为1和2的广义Steiner树问题的因子3/2逼近

1.25距离为1和2的Steiner树问题的近似算法

1.25 Approximation Algorithm for the Steiner Tree Problem with Distances One and Two

我们给出了距离为1和2的Steiner树问题的1.25近似算法，改进了该问题的最佳已知界。

Steiner Trees for Hereditary Graph Classes: a Treewidth Perspective

We consider the classical problems (Edge) Steiner Tree and Vertex Steiner Tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs. We show a dichotomy for the former problem restricted to $(H_1,H_2)$-free graphs and a dichotomy for the latter problem restricted to $H$-free graphs. We find that there exists an infinite family of graphs $H$ such that Vertex Steiner Tree is polynomial-time solvable for $H$-free graphs, whereas there exist only two graphs $H$ for which this holds for Edge Steiner Tree. We also find that Edge Steiner Tree…

k-Prize收集Steiner树问题的4-近似算法

A 4-Approximation Algorithm for k-Prize Collecting Steiner Tree Problems

本文研究了k-奖Steiner树问题的一个4-近似算法。这个问题推广了k-最小生成树问题和获奖Steiner树问题。我们提出的算法采用两个2-近似算法的k-最小生成树问题和奖金收集Steiner树问题。此外，我们的算法框架可以应用到一个特殊的情况下，k奖收集旅行商问题。

具有少量Steiner顶点的Steiner树的参数化近似方案

Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices

本文提出了一种针对具有少量Steiner顶点的Steiner树问题的高效参数化近似方案，并探讨了其在其他变种问题中的应用与限制。

A 2-approximation for the $k$-prize-collecting Steiner tree problem

We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which minimizes the cost of the edges in the tree plus the penalties of vertices not in the tree. This is one of the most fundamental network design problems and is a common generalization of the prize-collecting Steiner tree and the $k$-minimum spanning tree problems. Our main result is a 2-approximation algorithm, which improves on the currently best known approximatio…

关于近凸点集上欧几里得Steiner最小树的高效算法

Efficient Algorithms for Euclidean Steiner Minimal Tree on Near-Convex Terminal Sets

本文研究近凸点集上的欧几里得Steiner最小树问题，提出了多项式时间可解的显式结构，给出了基于非凸包点数的精确算法，并证明了FPTAS存在与不存在的条件。