Document Open Access Logo

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

Authors Loukas Georgiadis, Giuseppe F. Italiano, Aikaterini Karanasiou

PDF

File

Thumbnail PDF
PDF
LIPIcs.SEA.2017.9.pdf
  • Filesize: 0.68 MB
  • 16 pages

Document Identifiers

Subject Classification

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

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.

Cite As Get BibTex

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

Author Details

Loukas Georgiadis
Giuseppe F. Italiano
Aikaterini Karanasiou

References

  1. S. Alstrup, D. Harel, P. W. Lauridsen, and M. Thorup. Dominators in linear time. SIAM Journal on Computing, 28(6):2117-32, 1999. Google Scholar
  2. S. Baswana, K. Choudhary, and L. Roditty. Fault tolerant reachability for directed graphs. In Yoram Moses, editor, Distributed Computing, volume 9363 of Lecture Notes in Computer Science, pages 528-543. Springer Berlin Heidelberg, 2015. Google Scholar
  3. S. Baswana, K. Choudhary, and L. Roditty. Fault tolerant reachability subgraph: Generic and optimal. In Proc. Symposium on Theory of Computing, pages 509-518, 2016. Google Scholar
  4. A. L. Buchsbaum, L. Georgiadis, H. Kaplan, A. Rogers, R. E. Tarjan, and J. R. Westbrook. Linear-time algorithms for dominators and other path-evaluation problems. SIAM Journal on Computing, 38(4):1533-1573, 2008. Google Scholar
  5. J. Cheriyan and R. Thurimella. Approximating minimum-size k-connected spanning subgraphs via matching. SIAM J. Comput., 30(2):528-560, 2000. Google Scholar
  6. R. Cytron, J. Ferrante, B. K. Rosen, M. N. Wegman, and F. K. Zadeck. Efficiently computing static single assignment form and the control dependence graph. ACM Transactions on Programming Languages and Systems, 13(4):451-490, 1991. Google Scholar
  7. D. Delling, A. V. Goldberg, I. Razenshteyn, and R. F. Werneck. Graph partitioning with natural cuts. In 25th International Parallel and Distributed Processing Symposium (IPDPS'11), 2011. Google Scholar
  8. C. Demetrescu, A. V. Goldberg, and D. S. Johnson. 9th DIMACS Implementation Challenge: Shortest Paths, 2007. URL: http://www.dis.uniroma1.it/~challenge9/.
  9. J. Fakcharoenphol and B. Laekhanukit. An O(log²k)-approximation algorithm for the k-vertex connected spanning subgraph problem. In Proc. Symposium on Theory of Computing, STOC'08, pages 153-158, New York, NY, USA, 2008. ACM. Google Scholar
  10. D. R. Ford and D. R. Fulkerson. Flows in Networks. Princeton University Press, Princeton, NJ, USA, 2010. Google Scholar
  11. L. Georgiadis. Approximating the smallest 2-vertex connected spanning subgraph of a directed graph. In Proc. European Symposium on Algorithms, pages 13-24, 2011. Google Scholar
  12. L. Georgiadis, G. F. Italiano, A. Karanasiou, C. Papadopoulos, and N. Parotsidis. Sparse subgraphs for 2-connectivity in directed graphs. In Proc. Symposium on Experimental Algorithms, (SEA 2016), pages 150-166, 2016. Google Scholar
  13. L. Georgiadis, G. F. Italiano, C. Papadopoulos, and N. Parotsidis. Approximating the smallest spanning subgraph for 2-edge-connectivity in directed graphs. In Proc. European Symposium on Algorithms, pages 582-594, 2015. Google Scholar
  14. L. Georgiadis and R. E. Tarjan. Dominator tree certification and divergent spanning trees. ACM Transactions on Algorithms, 12(1):11:1-11:42, November 2015. Google Scholar
  15. L. Georgiadis and R. E. Tarjan. Addendum to "Dominator tree certification and divergent spanning trees". ACM Transactions on Algorithms, 12(4):56:1-56:3, August 2016. Google Scholar
  16. L. Georgiadis, R. E. Tarjan, and R. F. Werneck. Finding dominators in practice. Journal of Graph Algorithms and Applications (JGAA), 10(1):69-94, 2006. Google Scholar
  17. A. V. Goldberg and R. E. Tarjan. A new approach to the maximum-flow problem. Journal of the ACM, 35:921-940, October 1988. Google Scholar
  18. J. E. Hopcroft and R. M. Karp. An n^5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 2:225-231, 1973. Google Scholar
  19. G. F. Italiano, L. Laura, and F. Santaroni. Finding strong bridges and strong articulation points in linear time. Theoretical Computer Science, 447:74-84, 2012. Google Scholar
  20. S. Khuller, B. Raghavachari, and N. E. Young. Approximating the minimum equivalent digraph. SIAM J. Comput., 24(4):859-872, 1995. Announced at SODA 1994, 177-186. Google Scholar
  21. G. Kortsarz and Z. Nutov. Approximating minimum cost connectivity problems. Approximation Algorithms and Metaheuristics, 2007. Google Scholar
  22. Jérôme Kunegis. KONECT: the Koblenz network collection. In 22nd International World Wide Web Conference, WWW'13, Rio de Janeiro, Brazil, May 13-17, 2013, Companion Volume, pages 1343-1350, 2013. Google Scholar
  23. J. Leskovec and A. Krevl. SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data, June 2014.
  24. R. E. Tarjan. Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1(2):146-160, 1972. Google Scholar
  25. T. Tholey. Linear time algorithms for two disjoint paths problems on directed acyclic graphs. Theoretical Computer Science, 465:35-48, 2012. Google Scholar
  26. J. Zhao and S. Zdancewic. Mechanized verification of computing dominators for formalizing compilers. In Proc. 2nd International Conference on Certified Programs and Proofs, pages 27-42. Springer, 2012. Google Scholar
  27. L. Zhao, H. Nagamochi, and T. Ibaraki. A linear time 5/3-approximation for the minimum strongly-connected spanning subgraph problem. Information Processing Letters, 86(2):63-70, 2003. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact