A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesmen
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k MST problem (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Efficient recovery from power outage (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The budgeted maximum coverage problem
Information Processing Letters
Randomized metarounding (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximating k-median with non-uniform capacities
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Two Constant Approximation Algorithms for Node-Weighted Steiner Tree in Unit Disk Graphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Approximating Some Network Design Problems with Node Costs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximating Steiner networks with node weights
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Approximating Steiner Networks with Node-Weights
SIAM Journal on Computing
Approximating some network design problems with node costs
Theoretical Computer Science
Approximation schemes for node-weighted geometric steiner tree problems
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Approximating buy-at-bulk and shallow-light k-Steiner trees
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We consider a class of optimization problems, where the input is an undirected graph with two weight functions defined for each node, namely the node's profit and its cost. The goal is to find a connected set of nodes of low cost and high profit. We present approximation algorithms for three natural optimization criteria that arise in this context, all of which are NP-hard. The budget problem asks for maximizing the profit of the set subject to a budget constraint on its cost. The quota problem requires minimizing the cost of the set subject to a quota constraint on its profit. Finally, the prize collecting problem calls for minimizing the cost of the set plus the profit (here interpreted as a penalty) of the complement set. For all three problems, our algorithms give an approximation guarantee of O(\log n), where n is the number of nodes. To the best of our knowledge, these are the first approximation results for the quota problem and for the prize collecting problem, both of which are at least as hard to approximate as set cover. For the budget problem, our results improve on a previous O(\log^2 n) result of Guha, Moss, Naor, and Schieber. Our methods involve new theorems relating tree packings to (node) cut conditions. We also show similar theorems (with better bounds) using edge cut conditions. These imply bounds for the analogous budget and quota problems with edge costs which are comparable to known (constant factor) bounds.