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Approximation Algorithms for Steiner Connectivity Augmentation

Authors Daniel Hathcock , Michael Zlatin

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LIPIcs.ESA.2024.67.pdf
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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Approximation Algorithms
  • Steiner Connectivity
  • Network Design

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Abstract

We consider connectivity augmentation problems in the Steiner setting, where the goal is to augment the edge-connectivity between a specified subset of terminal nodes.
In the Steiner Augmentation of a Graph problem (k-SAG), we are given a k-edge-connected subgraph H of a graph G. The goal is to augment H by including links from G of minimum cost so that the edge-connectivity between nodes of H increases by 1. This is a generalization of the Weighted Connectivity Augmentation Problem, in which only links between pairs of nodes in H are available for the augmentation. 
In the Steiner Connectivity Augmentation Problem (k-SCAP), we are given a Steiner k-edge-connected graph connecting terminals R, and we seek to add links of minimum cost to create a Steiner (k+1)-edge-connected graph for R. Note that k-SAG is a special case of k-SCAP.
The results of Ravi, Zhang and Zlatin for the Steiner Tree Augmentation problem yield a (1.5+ε)-approximation for 1-SCAP and for k-SAG when k is odd [Ravi et al., 2023]. In this work, we give a (1 + ln{2} +ε)-approximation for the Steiner Ring Augmentation Problem (SRAP). This yields a polynomial time algorithm with approximation ratio (1 + ln{2} + ε) for 2-SCAP. We obtain an improved approximation guarantee for SRAP when the ring consists of only terminals, yielding a (1.5+ε)-approximation for k-SAG for any k.

Cite As Get BibTex

Daniel Hathcock and Michael Zlatin. Approximation Algorithms for Steiner Connectivity Augmentation. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 67:1-67:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.67

Author Details

Daniel Hathcock
  • Carnegie Mellon University, Pittsburgh, PA, USA
Michael Zlatin
  • Carnegie Mellon University, Pittsburgh, PA, USA

Funding

  • Hathcock, Daniel: Supported by the NSF Graduate Research Fellowship grant DGE-2140739.

References

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