Edge-Connectivity augmentation and network matrices

Authors:
Michele Conforti;Anna Galluccio;Guido Proietti
Affiliations:
Dipartimento di Matematica, Università di Padova, Padova, Italy;Istituto di Analisi dei Sistemi ed Informatica, CNR, Roma, Italy;Istituto di Analisi dei Sistemi ed Informatica, CNR, Roma, Italy
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

Citing 11
Cited 3

Theory of linear and integer programming

Theory of linear and integer programming
Edge-connectivity augmentation problems

Journal of Computer and System Sciences
Integer and combinatorial optimization

Integer and combinatorial optimization
Applications of a poset representation to edge connectivity and graph rigidity

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Augmenting graphs to meet edge-connectivity requirements

SIAM Journal on Discrete Mathematics
Approximation algorithms for graph augmentation

Journal of Algorithms
Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality

Mathematical Programming: Series A and B
Approximating covering and packing problems: set cover, vertex cover, independent set, and related problems

Approximation algorithms for NP-hard problems
Approximation algorithms for finding highly connected subgraphs

Approximation algorithms for NP-hard problems
An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning tree

Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
A 3/2-Approximation Algorithm for Augmenting the Edge-Connectivity of a Graph from 1 to 2 Using a Subset of a Given Edge Set

APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization

Reliability as an interdomain service

Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
Mixed models for the analysis of local search components

SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the following NP-hard graph augmentation problem: Given a weighted graph G and a connected spanning subgraph H of G, find a minimum weight set of edges of G to be added to H so that H becomes 2-edge-connected. We provide a formulation of the problem as a set covering problem, and we analyze the conditions for which the linear programming relaxation of our formulation always gives an integer solution. This yields instances of the problem that can be solved in polynomial time. As we will show in the paper, these particular instances have not only theoretical but also practical interest, since they model a wide range of survivability problems in communication networks.