Approximation algorithms for NP-hard problems
Combinatorial optimization
Improved performance of the greedy algorithm for partial cover
Information Processing Letters
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Constrained weighted matchings and edge coverings in graphs
Discrete Applied Mathematics
Using homogeneous weights for approximating the partial cover problem
Journal of Algorithms
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computational Complexity of Machine Learning
Computational Complexity of Machine Learning
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
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
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
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
Polyhedral techniques for graphic covering problems
Polyhedral techniques for graphic covering problems
A general approach to online network optimization problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation
Mathematical Programming: Series A and B
Approximation algorithms for partial covering problems
Journal of Algorithms
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
On approximation of the submodular set cover problem
Operations Research Letters
Theoretical Computer Science
Approximation algorithms for partially covering with edges
Theoretical Computer Science
Approximating Generalized Multicut on Trees
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
On Lagrangian Relaxation and Subset Selection Problems
Approximation and Online Algorithms
Monotone Covering Problems with an Additional Covering Constraint
Mathematics of Operations Research
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
FPTAS's for some cut problems in weighted trees
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
A Partial Set Covering Model for Protein Mixture Identification Using Mass Spectrometry Data
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
An Extension of the Nemhauser-Trotter Theorem to Generalized Vertex Cover with Applications
SIAM Journal on Discrete Mathematics
Extension of the nemhauser and trotter theorem to generalized vertex cover with applications
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
FPTASs for trimming weighted trees
Theoretical Computer Science
The maximum vertex coverage problem on bipartite graphs
Discrete Applied Mathematics
An iterated-tabu-search heuristic for a variant of the partial set covering problem
Journal of Heuristics
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An instance of the generalized partial cover problem consists of a ground set U and a family of subsets S⊆2U. Each element e ∈ U is associated with a profit p(e), whereas each subset S∈S has a cost c(S). The objective is to find a minimum cost subcollection S'⊆S such that the combined profit of the elements covered by S' is at least p, a specified profit bound. In the Drize-collecting version of this problem, there is no strict requirement to cover any element; however, if the subsets we pick leave an element e ∈ U uncovered, we incur a penalty of n(e). The goal is to identify a subcollection S'⊆S that minimizes the cost of S' plus the penalties of uncovered elements. Although problem-specific connections between the partial cover and the prize-collecting variants of a given covering problem have been explored and exploited, a more general connection remained open. The main contribution of this paper is to establish a formal relationship between these two variants. As a result, we present a unified framework for approximating problems that can be formulated or interpreted as special cases of generalized partial cover. We demonstrate the applicability of our method on a diverse collection of covering problems, for some of which we obtain the first non-trivial approximability results.