eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-09-04
19:1
19:16
10.4230/LIPIcs.APPROX/RANDOM.2023.19
article
Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem
Foos, Josefine
1
Held, Stephan
1
https://orcid.org/0000-0003-2188-1559
Spitzley, Yannik Kyle Dustin
1
https://orcid.org/0009-0001-2389-0048
Research Institute for Discrete Mathematics and Hausdorff Center for Mathematics, University of Bonn, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol275-approx-random2023/LIPIcs.APPROX-RANDOM.2023.19/LIPIcs.APPROX-RANDOM.2023.19.pdf
cost-distance Steiner tree
approximation algorithm
uniform