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On Lagrangian relaxation and subset selection problems
 In Proc. 6th Workshop on Approximation and Online Algorithms
, 2009
"... 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 ..."
Abstract

Cited by 2 (1 self)
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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 ρapproximation algorithm for the Lagrangian relaxation of the problem, for some ρ ∈ (0, 1), then our technique ρ ρ+1 achieves a ratio of −ε to the optimal, and this ratio is tight. The number of calls to the ρapproximation 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 realtime scheduling, the maximum generalized assignment problem (GAP) and maximum weight independent set. 1