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Parameterized Algorithms for Node Connectivity Augmentation Problems

Author Zeev Nutov

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

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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

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.

Subject Classification

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

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