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

Authors:
Xianyue Li;Xiao-Hua Xu;Feng Zou;Hongwei Du;Pengjun Wan;Yuexuan Wang;Weili Wu
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, China 730000;Department of Computer Science, Illinois Institute of Technology, Chicago, USA IL 60616;Department of Computer Science, University of Texas at Dallas, Richardson, USA TX 75080;Department of Computer Science, Illinois Institute of Technology, Chicago, USA IL 60616;Department of Computer Science, Illinois Institute of Technology, Chicago, USA IL 60616;Institute of Theoretical Computer Science, Tsinghua University, Beijing, China 100084;Department of Computer Science, University of Texas at Dallas, Richardson, USA TX 75080
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

Citing 14
Cited 2

Approximation algorithms for NP-complete problems on planar graphs

Journal of the ACM (JACM)
On the maximum degree of minimum spanning trees

SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Improved approximations for the Steiner tree problem

SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A nearly best-possible approximation algorithm for node-weighted Steiner trees

Journal of Algorithms
Approximation schemes for covering and packing problems in image processing and VLSI

Journal of the ACM (JACM)
Improved methods for approximating node weighted Steiner trees and connected dominating sets

Information and Computation
A 1.598 approximation algorithm for the Steiner problem in graphs

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved Steiner tree approximation in graphs

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximations for Steiner trees with minimum number of Steiner points

Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimum connected dominating sets and maximal independent sets in unit disk graphs

Theoretical Computer Science
Two Constant Approximation Algorithms for Node-Weighted Steiner Tree in Unit Disk Graphs

COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
A 5+epsilon (Porson)-approximation algorithm for minimum weighted dominating set in unit disk graph

Theoretical Computer Science
Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs

APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation

PTAS for minimum weighted connected vertex cover problem with c-local condition in unit disk graphs

Journal of Combinatorial Optimization
Primal-dual approximation algorithms for Node-Weighted Steiner Forest on planar graphs

Information and Computation

Quantified Score

Hi-index	0.00

Visualization

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+*** )-approximation algorithm for any *** 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 + *** )-approximation algorithm.