Approximations for node-weighted Steiner tree in unit disk graphs
نویسندگان
چکیده
Given a node-weighted connected graph and a subset of terminals, the problem node-weighted Steiner tree (NWST) seeks a lightest tree connecting a given set of terminals in a node-weighted graph. While NWST in general graphs are as hard as Set Cover, NWST restricted to unit-disk graphs (UDGs) admits X. Xu, H. Du, P.-J. Wan were supported in part by NSF under grant CNS-0831831. Y. Wang was supported in part by the National Basic Research Program of China Grants 2007CB807900 and 2007CB807901, NSFC under Grant 60604033, and the Hi-Tech Research Development Program of China Grant 2006AA10Z216. X. Xu · H. Du · P.-J. Wan (B) Department of Computer Science, Illinois Institute of Technology, Chicago, USA e-mail: [email protected] X. Xu e-mail: [email protected] H. Du e-mail: [email protected] Y. Wang Institute of Theoretical Computer Science, Tsinghua University, Beijing, People’s Republic of China e-mail: [email protected] F. Zou · W. Wu Department of Computer Science, University of Texas at Dallas, Richardson, USA e-mail: [email protected] W. Wu e-mail: [email protected] X. Li School of Mathematics and Statistics, Lanzhou University, Lanzhou, People’s Republic of China e-mail: [email protected]
منابع مشابه
A PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs
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...
متن کاملNode-weighted Steiner tree approximation in unit disk graphs
Given a graph G = (V ,E) with node weight w : V → R+ and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a < 1 unless NP ⊆ DTIME(nO(logn)), wher...
متن کاملNew approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs
Given a node-weighted graph, the minimum-weighted dominating set (MWDS) problem is to find a minimum-weighted vertex subset such that, for any vertex, it is contained in this subset or it has a neighbor contained in this set. And the minimum-weighted connected dominating set (MWCDS) problem is to find a MWDS such that the graph induced by this subset is connected. In this paper, we study these ...
متن کاملTwo Constant Approximation Algorithms for Node-Weighted Steiner Tree in Unit Disk Graphs
Given a graph G = (V,E) with node weight w : V → R and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a < 1 unless NP ⊆ DTIME(n), where n is th...
متن کاملA (4 + ǫ)-Approximation for the Minimum-Weight Dominating Set Problem in Unit Disk Graphs
We present a (4 + ǫ)-approximation algorithm for the problem of computing a minimum-weight dominating set in unit disk graphs, where ǫ is an arbitrarily small constant. The previous best known approximation ratio was 5+ǫ. The main result of this paper is a 4-approximation algorithm for the problem restricted to constant-size areas. To obtain the (4 + ǫ)-approximation algorithm for the unrestric...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Optimization Letters
دوره 4 شماره
صفحات -
تاریخ انتشار 2010