New Approximation Algorithms for the Steiner Tree Problems

The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solutions. We achieve the best up to now approximation ratios of 1.644 in arbitrary metric and 1.267 in rectilinear plane, respectively.

[1]  Marek Karpinski,et al.  1.757 and 1.267 - Approximation Algorithms for the Network and Rectilinear Steiner Tree Problems , 1994, Electron. Colloquium Comput. Complex..

[2]  A. Kahng,et al.  On optimal interconnections for VLSI , 1994 .

[3]  Q. Feng,et al.  On better heuristic for Euclidean Steiner minimum trees , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[4]  Jeffrey S. Salowe,et al.  An exact rectilinear Steiner tree algorithm , 1993, Proceedings of 1993 IEEE International Conference on Computer Design ICCD'93.

[5]  Ding-Zhu Du,et al.  The k-Steiner Ratio in Graphs , 1997, SIAM J. Comput..

[6]  F. Hwang.  On Steiner Minimal Trees with Rectilinear Distance , 1976 .

[7]  Kurt Mehlhorn,et al.  A Faster Approximation Algorithm for the Steiner Problem in Graphs , 1988, Inf. Process. Lett..

[8]  Michael Kaufmann,et al.  Faster Approximation Algorithms for the Rectilinear Steiner Tree Problem , 1993, ISAAC.

[9]  David S. Johnson,et al.  The Rectilinear Steiner Tree Problem is NP Complete , 1977, SIAM Journal of Applied Mathematics.

[10]  Marshall W. Bern,et al.  The Steiner Problem with Edge Lengths 1 and 2 , 1989, Inf. Process. Lett..

[11]  H. Pollak,et al.  Steiner Minimal Trees , 1968 .

[12]  Piotr Berman,et al.  Improved approximations for the Steiner tree problem , 1992, SODA '92.

[13]  Michael Kaufmann,et al.  Faster Approximation Algorithms for the Rectilinear Steiner Tree Problem , 1993, ISAAC.

[14]  Frank K. Hwang,et al.  An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees , 1979, JACM.

[15]  Marek Karpinski,et al.  Approaching the 5/4-Approximation for Rectilinear Steiner Trees , 1994, ESA.

[16]  A. Zelikovsky.  Better approximation bounds for the network and Euclidean Steiner tree problems , 1996 .

[17]  Alex Zelikovsky.  A Faster Approximation Algorithm for the Steiner Tree Problem in Graphs , 1993, Inf. Process. Lett..

[18]  D. Eppstein,et al.  Approximation algorithms for geometric problems , 1996 .

[19]  David S. Johnson,et al.  The Rectilinear Steiner Problem is NP-Complete , 1977 .