Faster approximation algorithms for weighted triconnectivity augmentation problems

Zeev Nutov; Michal Penn

doi:10.1016/S0167-6377(97)00045-X

Faster approximation algorithms for weighted triconnectivity augmentation problems

Research output: Contribution to journal › Article › peer-review

Abstract

The problem of finding a minimum-weight augmenting edge-set to make a graph 3-vertex connected is considered. This problem is known to be NP-complete. We present a new 3-approximation algorithm for making an arbitrary graph 3-vertex connected. Our algorithm is simpler and faster than the previously known 3-approximation algorithm by a factor of O(n²), where n is the number of vertices of the graph. We also consider the problem of increasing the vertex-connectivity of a 2-connected graph from 2 to 3.

Original language	English
Pages (from-to)	219-223
Number of pages	5
Journal	Operations Research Letters
Volume	21
Issue number	5
DOIs	https://doi.org/10.1016/S0167-6377(97)00045-X
State	Published - 12 Jan 1997
Externally published	Yes

Bibliographical note

Funding Information:
We are grateful to Rafi Hassin for many stimulating discussion. Partial support was received from the Technion fund for promotion of research.

Keywords

Approximation algorithm
Augmentation problem
Graph
Vertex connectivity

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10.1016/S0167-6377(97)00045-X

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title = "Faster approximation algorithms for weighted triconnectivity augmentation problems",

abstract = "The problem of finding a minimum-weight augmenting edge-set to make a graph 3-vertex connected is considered. This problem is known to be NP-complete. We present a new 3-approximation algorithm for making an arbitrary graph 3-vertex connected. Our algorithm is simpler and faster than the previously known 3-approximation algorithm by a factor of O(n2), where n is the number of vertices of the graph. We also consider the problem of increasing the vertex-connectivity of a 2-connected graph from 2 to 3.",

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AU - Penn, Michal

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N2 - The problem of finding a minimum-weight augmenting edge-set to make a graph 3-vertex connected is considered. This problem is known to be NP-complete. We present a new 3-approximation algorithm for making an arbitrary graph 3-vertex connected. Our algorithm is simpler and faster than the previously known 3-approximation algorithm by a factor of O(n2), where n is the number of vertices of the graph. We also consider the problem of increasing the vertex-connectivity of a 2-connected graph from 2 to 3.

AB - The problem of finding a minimum-weight augmenting edge-set to make a graph 3-vertex connected is considered. This problem is known to be NP-complete. We present a new 3-approximation algorithm for making an arbitrary graph 3-vertex connected. Our algorithm is simpler and faster than the previously known 3-approximation algorithm by a factor of O(n2), where n is the number of vertices of the graph. We also consider the problem of increasing the vertex-connectivity of a 2-connected graph from 2 to 3.

KW - Approximation algorithm

KW - Augmentation problem

KW - Graph

KW - Vertex connectivity

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JO - Operations Research Letters

JF - Operations Research Letters

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Faster approximation algorithms for weighted triconnectivity augmentation problems

Abstract

Bibliographical note

Keywords

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