Algorithmica

, Volume 70, Issue 4, pp 648–674 | Cite as

A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs

Article

Abstract

We give an approximation algorithm for fractional packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm (with high probability) computes feasible primal and dual solutions whose costs are within a factor of 1+ε of opt (the optimal cost) in time O((r+c)log(n)/ε2+n).

Keywords

Linear programming Packing Covering Lagrangian relaxation Approximation algorithm Linear time Lagrangian relaxation 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of CaliforniaRiversideUSA

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