Many birds with one stone: multi-objective approximation algorithms
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Bicriteria network design problems
Journal of Algorithms
A deterministic algorithm for the cost-distance problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Simultaneous optimization for concave costs: single sink aggregation or single source buy-at-bulk
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Rapid rumor ramification: approximating the minimum broadcast time
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Stochastic Steiner Tree with Non-uniform Inflation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation schemes for multi-budgeted independence systems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
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We describe a very simple idea for designing approximation algorithms for connectivity problems: For a spanning tree problem, the idea is to start with the empty set of edges, and add matching paths between pairs of components in the current graph that have desirable properties in terms of the objective function of the spanning tree problem being solved. Such matching augment the solution by reducing the number of connected components to roughly half their original number, resulting in a logarithmic number of such matching iterations. A logarithmic performance ratio results for the problem by appropriately bounding the contribution of each matching to the objective function by that of an optimal solution. In this survey, we trace the initial application of these ideas to traveling salesperson problems through a simple tree pairing observation down to more sophisticated applications for buy-at-bulk type network design problems.