Send-and-split method for minimum-concave-cost network flows
Mathematics of Operations Research
A faster approximation algorithm for the Steiner problem in graphs
Information Processing Letters
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
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)
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth 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
Improved algorithms for the Steiner problem in networks
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Obstacle-Avoiding Euclidean Steiner Trees in the Plane: An Exact Algorithm
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
On the Implementation of MST-Based Heuristics for the Steiner Problem in Graphs
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Extending Reduction Techniques for the Steiner Tree Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A linear-time approximation scheme for planar weighted TSP
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Highly scalable algorithms for rectilinear and octilinear Steiner trees
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A subset spanner for Planar graphs,: with application to subset TSP
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A polynomial-time approximation scheme for Steiner tree in planar graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The Two-Edge Connectivity Survivable Network Problem in Planar Graphs
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Discrete Applied Mathematics
An O(n log n) approximation scheme for Steiner tree in planar graphs
ACM Transactions on Algorithms (TALG)
A near linear time approximation scheme for Steiner tree among obstacles in the plane
Computational Geometry: Theory and Applications
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Practical partitioning-based methods for the steiner problem
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
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We present the first attempt on implementing a highly theoretical polynomial-time approximation scheme (PTAS) with huge hidden constants, namely, the PTAS for Steiner tree in planar graphs by Borradaile, Klein, and Mathieu (2009). Whereas this result, and several other PTAS results of the recent years, are of high theoretical importance, no practical applications or even implementation attempts have been known to date, due to the extremely large constants that are involved in them. We describe techniques on how to circumvent the challenges in implementing such a scheme. With today's limitations on processing power and space, we still have to sacrifice approximation guarantees for improved running times by choosing some parameters empirically. But our experiments show that with our choice of parameters, we do get the desired approximation ratios, suggesting that a much tighter analysis might be possible. Our computational experiments with benchmark instances from SteinLib and large artificial instances well exceeded our own expectations. We demonstrate that we are able to handle instances with up to a million nodes and several hundreds of terminals in 1.5 hours on a standard PC. On the rectilinear preprocessed instances from SteinLib, we observe a monotonous improvement for smaller values of ε, with an average gap below 1% for ε = 0.1. We compare our implementation against the well-known batched 1-Steiner heuristic and observe that on very large instances, we are able to produce comparable solutions much faster. We also present a thorough experimental evaluation of the influence of the various parameters of the PTAS and thus obtain a better understanding of their empirical effects.