A faster approximation algorithm for the Steiner problem in graphs
Acta Informatica
Fast algorithms for direct enclosures and direct dominances
Journal of Algorithms
Improved approximations for the Steiner tree problem
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Computing optimal rectilinear Steiner trees: a survey and experimental evaluation
Discrete Applied Mathematics - Special volume on VLSI
On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
RNC-Approximation Algorithms for the Steiner Problem
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Solving Rectilinear Steiner Tree Problems Exactly in Theory and Practice
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Efficient Steiner tree construction based on spanning graphs
Proceedings of the 2003 international symposium on Physical design
Proceedings of the 2003 ACM symposium on Applied computing
Fast and accurate rectilinear steiner minimal tree algorithm for VLSI design
Proceedings of the 2005 international symposium on Physical design
Demand-scalable geographic multicasting in wireless sensor networks
Computer Communications
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
| Hi-index | 0.00 |
The minimum rectilinear Steiner tree (RST) problem is one of the fundamental problems in the field of electronic design automation. The problem is NP-hard, and much work has been devoted to designing good heuristics and approximation algorithms; to date, the champion in solution quality among RST heuristics is the Batched Iterated 1-Steiner (BI1S) heuristic of Kahng and Robins. In a recent development, exact RST algorithms have witnessed spectacular progress: The new release of the GeoSteiner code of Warme, Winter, and Zachariasen has average running time comparable to that of the fastest available BI1S implementation, due to Robins. We are thus faced with the paradoxical situation that an exact algorithm for an NP-hard problem is competitive in speed with a state-of-the-art heuristic for the problem.The main contribution of this paper is a new RST heuristic, which has at its core a recent 3/2 approximation algorithm of Rajagopalan and Vazirani for the metric Steiner tree problem on quasi-bipartite graphs—these are graphs that do not contain edges connecting paris of Steiner vertices. The RV algorithm is built around the linear programming relaxation of a sophisticated integer program formulation, called the bidirected cut relaxation. Our heuristic achieves a good running time by combining an efficient implementation of the RV algorithm with simple, but powerful geometric reductions.Experiments conducted on both random and real VLSI instances show that the new RST heuristic runs significantly faster than Robins' implementation of BI1S and than the GeoSteiner code. Moreover, the new heuristic typically gives higher-quality solutions than BI1S.