Computational Complexity
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees
SIAM Journal on Computing
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Approximations of Independent Sets in Graphs
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An efficient approximation for the generalized assignment problem
Information Processing Letters
Real-Time Scheduling with a Budget
Algorithmica
Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems
Mathematics of Operations Research
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Primal-dual algorithms for combinatorial optimization problems
Primal-dual algorithms for combinatorial optimization problems
Resource Allocation in Bounded Degree Trees
Algorithmica
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Algorithms and complexity for periodic real-time scheduling
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and complexity for periodic real-time scheduling
ACM Transactions on Algorithms (TALG)
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We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of subset selection problems with linear constraints. Given a problem in this class and some small ε ∈ (0,1), we show that if there exists a ρ-approximation algorithm for the Lagrangian relaxation of the problem, for some ρ ∈ (0,1), then our technique achieves a ratio of $\frac{\rho}{\rho+1} -\! \varepsilon$ to the optimal, and this ratio is tight. The number of calls to the ρ-approximation algorithm, used by our algorithms, is linear in the input size and in log(1 / ε) for inputs with cardinality constraint, and polynomial in the input size and in log(1 / ε) for inputs with arbitrary linear constraint. Using the technique we obtain approximation algorithms for natural variants of classic subset selection problems, including real-time scheduling, the maximum generalized assignment problem (GAP) and maximum weight independent set.