TY - GEN

T1 - Improved approximations for the steiner tree problem

AU - Berman, Piotr

AU - Ramaiyer, Viswanathan

PY - 1992/9/1

Y1 - 1992/9/1

N2 - For a set S contained in a metric space, a Steiner tree of S is a tree that connects the points in S. Finding a minimum cost Steiner tree is an NP-hard problem in euclidean and rectilinear metrics as well as in graphs. We give an approximation algorithm and show that the worst-case ratio of the cost of our solutions to the optimal cost is better than previously known ratios in graphs, and in rectilinear metric on the plane. Our method offers a tradeoff between the running time and the ratio; on one hand it always allows to improve the ratio, on the other it allows to obtain previously known ratios with much greater efficiency. We use properties of optimal rectilinear Steiner trees to obtain significantly better ratio and running time in rectilinear metric.

AB - For a set S contained in a metric space, a Steiner tree of S is a tree that connects the points in S. Finding a minimum cost Steiner tree is an NP-hard problem in euclidean and rectilinear metrics as well as in graphs. We give an approximation algorithm and show that the worst-case ratio of the cost of our solutions to the optimal cost is better than previously known ratios in graphs, and in rectilinear metric on the plane. Our method offers a tradeoff between the running time and the ratio; on one hand it always allows to improve the ratio, on the other it allows to obtain previously known ratios with much greater efficiency. We use properties of optimal rectilinear Steiner trees to obtain significantly better ratio and running time in rectilinear metric.

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M3 - Conference contribution

AN - SCOPUS:84990728999

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 325

EP - 334

BT - Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992

PB - Association for Computing Machinery

T2 - 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992

Y2 - 27 January 1992 through 29 January 1992

ER -