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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.19

Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem

Authors: Josefine Foos, Stephan Held, and Yannik Kyle Dustin Spitzley

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract

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.

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Josefine Foos, Stephan Held, and Yannik Kyle Dustin Spitzley. Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{foos_et_al:LIPIcs.APPROX/RANDOM.2023.19,
  author =	{Foos, Josefine and Held, Stephan and Spitzley, Yannik Kyle Dustin},
  title =	{{Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.19},
  URN =		{urn:nbn:de:0030-drops-188443},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.19},
  annote =	{Keywords: cost-distance Steiner tree, approximation algorithm, uniform}
}

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Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem

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