A PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs

Abstract. The node-weighted Steiner tree problem is a variation of classical Steiner minimum tree problem. Given a graph G = (V, E) with node weight function C : V → R+ and a subset X of V , the node-weighted Steiner tree problem is to find a Steiner tree for the set X such that its total weight is minimum. In this paper, we study this problem in unit disk graphs and present a (1+ε)-approximation algorithm for any ε > 0, when the given set of vertices is c-local. As an application, we use node-weighted Steiner tree to solve the node-weighted connected dominating set problem in unit disk graphs and obtain a (5+ε)-approximation algorithm.

• Type: Conference
• Year: 2009
• Where: COCOA
• Authors: Xianyue Li, Xiao-Hua Xu, Feng Zou, Hongwei Du, Peng-Jun Wan, Yuexuan Wang, Weili Wu
• Keywords: COCOA 2009, Discrete Geometry, Node-weighted Steiner Tree, Steiner Minimum Tree, Steiner Tree Problem