Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
An approximation scheme for finding Steiner trees with obstacles
SIAM Journal on Computing
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
On wirelength estimations for row-based placement
ISPD '98 Proceedings of the 1998 international symposium on Physical design
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The X architecture: not your father's diagonal wiring
SLIP '02 Proceedings of the 2002 international workshop on System-level interconnect prediction
Minimum Networks in Uniform Orientation Metrics
SIAM Journal on Computing
Estimation of wirelength reduction for λ-geometry vs. manhattan placement and routing
Proceedings of the 2003 international workshop on System-level interconnect prediction
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
An Exact Algorithm for the Uniformly-Oriented Steiner Tree Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
I/o-efficient algorithms for shortest path related problems
I/o-efficient algorithms for shortest path related problems
A new paradigm for general architecture routing
Proceedings of the 14th ACM Great Lakes symposium on VLSI
Highly scalable algorithms for rectilinear and octilinear Steiner trees
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Algorithms and complexity analyses for some combinatorial optimization problems
Algorithms and complexity analyses for some combinatorial optimization problems
A polynomial-time approximation scheme for Steiner tree in planar graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric intersection problems
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
Approximation of octilinear steiner trees constrained by hard and soft obstacles
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Dealing with large hidden constants: engineering a planar steiner tree PTAS
Journal of Experimental Algorithmics (JEA)
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We present a polynomial-time approximation scheme (PTAS) for the Steiner tree problem with polygonal obstacles in the plane with running time O(nlog^2n), where n denotes the number of terminals plus obstacle vertices. To this end, we show how a planar spanner of size O(nlogn) can be constructed that contains a (1+@e)-approximation of the optimal tree. Then one can find an approximately optimal Steiner tree in the spanner using the algorithm of Borradaile et al. (2007) for the Steiner tree problem in planar graphs. We prove this result for the Euclidean metric and also for all uniform orientation metrics, i.e. particularly the rectilinear and octilinear metrics.