Introduction to algorithms
Easy problems for tree-decomposable graphs
Journal of 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 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 algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
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
Improved Approximation Algorithms for the Partial Vertex Cover Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Distributions on Level-Sets with Applications to Approximation Algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Energy and quality aware query processing in wireless sensor database systems
Information Sciences: an International Journal
Theoretical Computer Science
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
International Journal of Autonomous and Adaptive Communications Systems
A 6/5-Approximation Algorithm for the Maximum 3-Cover Problem
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On generating near-optimal tableaux for conditional functional dependencies
Proceedings of the VLDB Endowment
Improved Upper Bounds for Partial Vertex Cover
Graph-Theoretic Concepts in Computer Science
Proceedings of the 19th international conference on World wide web
Approximation of partial capacitated vertex cover
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Some results on incremental vertex cover problem
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Thresholded covering algorithms for robust and max-min optimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Information Processing Letters
A Partial Set Covering Model for Protein Mixture Identification Using Mass Spectrometry Data
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
SIAM Journal on Computing
Subexponential algorithms for partial cover problems
Information Processing Letters
Implicit branching and parameterized partial cover problems
Journal of Computer and System Sciences
Resource allocation for covering time varying demands
ESA'11 Proceedings of the 19th European conference on Algorithms
Survey: Covering problems in facility location: A review
Computers and Industrial Engineering
Approximation of Partial Capacitated Vertex Cover
SIAM Journal on Discrete Mathematics
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Covering analysis of the greedy algorithm for partial cover
Algorithms and Applications
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
On the inapproximability of maximum intersection problems
Information Processing Letters
Set cover revisited: hypergraph cover with hard capacities
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Journal of Discrete Algorithms
A 6/5-approximation algorithm for the maximum 3-cover problem
Journal of Combinatorial Optimization
A randomised approximation algorithm for the partial vertex cover problem in hypergraphs
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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We study a generalization of covering problems called 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-partial set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-partial 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-partial vertex cover) in polynomial time. Without making any assumption about the number of sets an element is in, 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-partial 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-partial vertex cover on planar graphs, and for covering k points in Rd by disks.