Introduction to algorithms
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A modified greedy heuristic for the set covering problem with improved worst case bound
Information Processing Letters
A primal-dual parallel approximation technique applied to weighted set and vertex covers
Journal of Algorithms
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
The hardness of approximation: gap location
Computational Complexity
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved performance of the greedy algorithm for partial cover
Information Processing Letters
The Lovász Theta Function and a Semidefinite Programming Relaxation of Vertex Cover
SIAM Journal on Discrete Mathematics
Using homogenous weights for approximating the partial cover problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
New approaches to covering and packing problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computational Complexity of Machine Learning
Computational Complexity of Machine Learning
Approximating k-Set Cover and Complementary Graph Coloring
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
The t-Vertex Cover Problem: Extending the Half Integrality Framework with Budget Constraints
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Improved Approximation Algorithms for the Partial Vertex Cover Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Survey: Covering problems in facility location: A review
Computers and Industrial Engineering
A General Approach for Incremental Approximation and Hierarchical Clustering
SIAM Journal on Computing
A primal-dual approximation algorithm for partial vertex cover: making educated guesses
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
Submodular integer cover and its application to production planning
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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We study the generalization of covering problems to partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-set cover, if each element occurs in at most f sets, then we derive a primal-dual f-approximation algorithm (thus implying a 2-approximation for k-vertex cover) in polynomial time. In addition to its simplicity, this algorithm has the advantage of being parallelizable. For instances where each set has cardinality at most three, we obtain an approximation of 4/3. We also present better-than-2-approximation algorithms for k-vertex cover on bounded degree graphs, and for vertex cover on expanders of bounded average degree. We obtain a polynomial-time approximation scheme for k-vertex cover on planar graphs, and for covering points in Rd by disks.