Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Improved approximations for the Steiner tree problem
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
On component-size bounded Steiner trees
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
SIAM Journal on Computing
On wirelength estimations for row-based placement
ISPD '98 Proceedings of the 1998 international symposium on Physical design
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
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
On the terminal Steiner tree problem
Information Processing Letters
A note on the terminal Steiner tree problem
Information Processing Letters
Theoretical Computer Science
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the partial terminal Steiner tree problem
The Journal of Supercomputing
Note: Approximating the selected-internal Steiner tree
Theoretical Computer Science
A Better Constant-Factor Approximation for Selected-Internal Steiner Minimum Tree
Algorithmica - Special Issue: Computation and Combinatorial Optimization; Guest Editors: Xiaodong Hu and Jie Wang
On the full and bottleneck full Steiner tree problems
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Algorithms for terminal steiner trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Min-cost flow-based algorithm for simultaneous pin assignment and routing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An Efficient Tile-Based ECO Router Using Routing Graph Reduction and Enhanced Global Routing Flow
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Given a graph G=(V,E) with a cost function c:E-R^+ and a vertex subset R@?V, an internal Steiner tree is a Steiner tree that contains all the vertices in R, and such that each vertex in R must be an internal vertex. The internal Steiner tree problem involves finding an internal Steiner tree T whose total cost @?"("u","v")"@?"E"("T")c(u,v) is the minimum. In this paper, we first show that the internal Steiner tree problem is MAX SNP-hard. We then present a (2@r+1)-approximation algorithm for solving the problem on complete graphs, where @r is an approximation ratio for the Steiner tree problem. Currently, the best-known @r is ln4+@e