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Approximating the Smallest 2-Vertex-Connected Spanning Subgraph via Low-High Orders

Authors Loukas Georgiadis, Giuseppe F. Italiano, Aikaterini Karanasiou

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Loukas Georgiadis
Giuseppe F. Italiano
Aikaterini Karanasiou

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Loukas Georgiadis, Giuseppe F. Italiano, and Aikaterini Karanasiou. Approximating the Smallest 2-Vertex-Connected Spanning Subgraph via Low-High Orders. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.SEA.2017.9

Abstract

Let G = (V, E) be a 2-vertex-connected directed graph with m edges and n vertices. We consider the problem of approximating the smallest 2-vertex connected spanning subgraph (2VCSS) of G, and provide new efficient algorithms for this problem based on a clever use of low-high orders. The best previously known algorithms were able to compute a 3/2-approximation in O(m n+n 2) time, or a 3-approximation faster in linear time. In this paper, we present a linear-time algorithm that achieves a better approximation ratio of 2, and another algorithm that matches the previous 3/2-approximation in O(m n + n 2 ) time. We conducted a thorough experimental evaluation of all the above algorithms on a variety of input graphs. The experimental results show that both our two new algorithms perform well in practice. In particular, in our experiments the new 3/2-approximation algorithm was always faster than the previous 3/2-approximation algorithm, while their two approximation ratios were close. On the other side, our new linear-time algorithm yielded consistently better approximation ratios than the previously known linear-time algorithm, at the price of a small overhead in the running time.

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Keywords
  • 2-vertex connectivity
  • approximation algorithms
  • directed graphs

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