Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem
Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or telecommunication networks. They are a special case of general cost-distance Steiner trees, where different distance functions are used for total length and path lengths.
We improve the best published approximation factor for the uniform cost-distance Steiner tree problem from 2.39 [Khazraei and Held, 2021] to 2.05. If we can approximate the minimum-length Steiner tree problem arbitrarily well, our algorithm achieves an approximation factor arbitrarily close to 1+1/√2. This bound is tight in the following sense. We also prove the gap 1+1/√2 between optimum solutions and the lower bound which we and all previous approximation algorithms for this problem use.
Similarly to previous approaches, we start with an approximate minimum-length Steiner tree and split it into subtrees that are later re-connected. To improve the approximation factor, we split it into components more carefully, taking the cost structure into account, and we significantly enhance the analysis.
cost-distance Steiner tree
approximation algorithm
uniform
Theory of computation~Approximation algorithms analysis
Theory of computation~Routing and network design problems
19:1-19:16
APPROX
https://arxiv.org/abs/2305.03381
Josefine
Foos
Josefine Foos
Research Institute for Discrete Mathematics and Hausdorff Center for Mathematics, University of Bonn, Germany
Stephan
Held
Stephan Held
Research Institute for Discrete Mathematics and Hausdorff Center for Mathematics, University of Bonn, Germany
https://orcid.org/0000-0003-2188-1559
Yannik Kyle Dustin
Spitzley
Yannik Kyle Dustin Spitzley
Research Institute for Discrete Mathematics and Hausdorff Center for Mathematics, University of Bonn, Germany
https://orcid.org/0009-0001-2389-0048
10.4230/LIPIcs.APPROX/RANDOM.2023.19
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Josefine Foos, Stephan Held, and Yannik Kyle Dustin Spitzley
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