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Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures

Authors Felix Hommelsheim , Zhenwei Liu , Nicole Megow , Guochuan Zhang

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ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Network Design
  • Edge Failures
  • Graph Connectivity
  • Approximation Algorithms

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Abstract

We study the problem of guaranteeing the connectivity of a given graph by protecting or strengthening edges. Herein, a protected edge is assumed to be robust and will not fail, which features a non-uniform failure model. We introduce the (p,q)-Steiner-Connectivity Preservation problem where we protect a minimum-cost set of edges such that the underlying graph maintains p-edge-connectivity between given terminal pairs against edge failures, assuming at most q unprotected edges can fail. We design polynomial-time exact algorithms for the cases where p and q are small and approximation algorithms for general values of p and q. Additionally, we show that when both p and q are part of the input, even deciding whether a given solution is feasible is NP-complete. This hardness also carries over to Flexible Network Design, a research direction that has gained significant attention. In particular, previous work focuses on problem settings where either p or q is constant, for which our new hardness result now provides justification.

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Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang. Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.51

Author Details

Felix Hommelsheim
  • University of Bremen, Germany
Zhenwei Liu
  • Zhejiang University, Hangzhou, China
  • University of Bremen, Germany
Nicole Megow
  • University of Bremen, Germany
Guochuan Zhang
  • Zhejiang University, Hangzhou, China

Funding

  • Liu, Zhenwei: Research supported in part by NSFC (No. 12271477).
  • Zhang, Guochuan: Research supported in part by NSFC (No. 12271477).

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