Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5

Yefim Dinitz; Zeev Nutov

doi:10.1007/3-540-62592-5_57

Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The problem of finding a minimum weight k-vertex connected spanning subgraph is considered. For k>1, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there are k internally vertex-disjoint paths to every other vertex), we derive polynomial time approximation algorithms for several values of k. (i) For k=3, we give an algorithm with approximation factor 2. This improves the best previously known factor 3. (ii) For k= 4 and k= 5, we give an algorithm with approximation factor 3.

Original language	English
Title of host publication	Algorithms and Complexity - 3rd Italian Conference, CIAC 1997, Proceedings
Editors	Giancarlo Bongiovanni, Daniel Pierre Bovet, Giuseppe Di Battista
Publisher	Springer Verlag
Pages	13-24
Number of pages	12
ISBN (Print)	3540625925, 9783540625926
DOIs	https://doi.org/10.1007/3-540-62592-5_57
State	Published - 1997
Externally published	Yes
Event	3rd Italian Conference on Algorithms and Complexity, CIAC 1997 - Rome, Italy Duration: 12 Mar 1997 → 14 Mar 1997

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1203
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd Italian Conference on Algorithms and Complexity, CIAC 1997
Country/Territory	Italy
City	Rome
Period	12/03/97 → 14/03/97

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

Access to Document

10.1007/3-540-62592-5_57

Cite this

Dinitz, Y., & Nutov, Z. (1997). Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5. In G. Bongiovanni, D. P. Bovet, & G. Di Battista (Eds.), Algorithms and Complexity - 3rd Italian Conference, CIAC 1997, Proceedings (pp. 13-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1203). Springer Verlag. https://doi.org/10.1007/3-540-62592-5_57

Dinitz, Yefim ; Nutov, Zeev. / Finding optimum k-vertex connected spanning subgraphs : Improved approximation algorithms for k=3, 4, 5. Algorithms and Complexity - 3rd Italian Conference, CIAC 1997, Proceedings. editor / Giancarlo Bongiovanni ; Daniel Pierre Bovet ; Giuseppe Di Battista. Springer Verlag, 1997. pp. 13-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The problem of finding a minimum weight k-vertex connected spanning subgraph is considered. For k>1, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there are k internally vertex-disjoint paths to every other vertex), we derive polynomial time approximation algorithms for several values of k. (i) For k=3, we give an algorithm with approximation factor 2. This improves the best previously known factor 3. (ii) For k= 4 and k= 5, we give an algorithm with approximation factor 3.",

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Dinitz, Y & Nutov, Z 1997, Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5. in G Bongiovanni, DP Bovet & G Di Battista (eds), Algorithms and Complexity - 3rd Italian Conference, CIAC 1997, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1203, Springer Verlag, pp. 13-24, 3rd Italian Conference on Algorithms and Complexity, CIAC 1997, Rome, Italy, 12/03/97. https://doi.org/10.1007/3-540-62592-5_57

Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5. / Dinitz, Yefim; Nutov, Zeev.
Algorithms and Complexity - 3rd Italian Conference, CIAC 1997, Proceedings. ed. / Giancarlo Bongiovanni; Daniel Pierre Bovet; Giuseppe Di Battista. Springer Verlag, 1997. p. 13-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1203).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Dinitz Y, Nutov Z. Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5. In Bongiovanni G, Bovet DP, Di Battista G, editors, Algorithms and Complexity - 3rd Italian Conference, CIAC 1997, Proceedings. Springer Verlag. 1997. p. 13-24. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-62592-5_57

Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5

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