License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SEA.2017.9
URN: urn:nbn:de:0030-drops-76299
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7629/
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Georgiadis, Loukas ; Italiano, Giuseppe F. ; Karanasiou, Aikaterini

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

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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.

BibTeX - Entry

@InProceedings{georgiadis_et_al:LIPIcs:2017:7629,
  author =	{Loukas Georgiadis and Giuseppe F. Italiano and Aikaterini Karanasiou},
  title =	{{Approximating the Smallest 2-Vertex-Connected Spanning Subgraph via Low-High Orders}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Costas S. Iliopoulos and Solon P. Pissis and Simon J. Puglisi and Rajeev Raman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7629},
  URN =		{urn:nbn:de:0030-drops-76299},
  doi =		{10.4230/LIPIcs.SEA.2017.9},
  annote =	{Keywords: 2-vertex connectivity,  approximation algorithms, directed graphs}
}

Keywords: 2-vertex connectivity, approximation algorithms, directed graphs
Collection: 16th International Symposium on Experimental Algorithms (SEA 2017)
Issue Date: 2017
Date of publication: 07.08.2017

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