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Bicriteria Approximation for k-Edge-Connectivity

Authors Zeev Nutov , Reut Cohen

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • k-edge-connected subgraph
  • bicriteria approximation
  • iterative LP-rounding

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Abstract

In the k-Edge Connected Spanning Subgraph (k-ECSS) problem we are given a (multi-)graph G = (V,E) with edge costs and an integer k, and seek a min-cost k-edge-connected spanning subgraph of G. The problem admits a 2-approximation algorithm and no better approximation ratio is known. Recently, Hershkowitz, Klein, and Zenklusen [STOC 24] gave a bicriteria (1,k-10)-approximation algorithm that computes a (k-10)-edge-connected spanning subgraph of cost at most the optimal value of a standard Cut-LP for k-ECSS. We improve the bicriteria approximation to (1,k-4) and also give another non-trivial bicriteria approximation (3/2,k-2).
The k-Edge-Connected Spanning Multi-subgraph (k-ECSM) problem is almost the same as k-ECSS, except that any edge can be selected multiple times at the same cost. A (1,k-p) bicriteria approximation for k-ECSS w.r.t. Cut-LP implies approximation ratio 1+p/k for k-ECSM, hence our result also improves the approximation ratio for k-ECSM.

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Zeev Nutov and Reut Cohen. Bicriteria Approximation for k-Edge-Connectivity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 66:1-66:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.66

Author Details

Zeev Nutov
  • The Open University of Israel, Ra'anana, Israel
Reut Cohen
  • The Open University of Israel, Ra'anana, Israel

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