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Parameterized Algorithms for Node Connectivity Augmentation Problems

Author Zeev Nutov

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • node connectivity augmentation
  • fixed-parameter tractability

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Abstract

A graph G is k-out-connected from its node s if it contains k internally disjoint sv-paths to every node v; G is k-connected if it is k-out-connected from every node. In connectivity augmentation problems, the goal is to augment a graph G₀ = (V,E₀) by a minimum costs edge set J such that G₀ ∪ J has higher connectivity than G₀. In the k-Out-Connectivity Augmentation ({k-OCA}) problem, G₀ is (k-1)-out-connected from s and G₀ ∪ J should be k-out-connected from s; in the k-Connectivity Augmentation ({k-CA}) problem G₀ is (k-1)-connected and G₀ ∪ J should be k-connected. The parameterized complexity status of these problems was open even for k = 3 and unit costs. We will show that {k-OCA} and 3-{CA} can be solved in time 9^p ⋅ n^{O(1)}, where p is the size of an optimal solution. Our paper is the first that shows fixed-parameter tractability of a k-node-connectivity augmentation problem with high values of k. We will also consider the (2,k)-Connectivity Augmentation ({(2,k)-CA}) problem where G₀ is (k-1)-edge-connected and G₀ ∪ J should be both k-edge-connected and 2-connected. We will show that this problem can be solved in time 9^p ⋅ n^{O(1)}, and for unit costs approximated within 1.892.

Cite As Get BibTex

Zeev Nutov. Parameterized Algorithms for Node Connectivity Augmentation Problems. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 92:1-92:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.92

Author Details

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

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