Abstract
Configuration-LPs have proved to be successful in the design and analysis of approximation algorithms for a variety of discrete optimization problems. In addition, lower bounds based on configuration-LPs are a tool of choice for many practitioners especially those solving transportation and bin packing problems. In this work we initiate a study of linear programming relaxations with exponential number of variables for unrelated parallel machine scheduling problems with total weighted sum of completion times objective. We design a polynomial time approximation scheme to solve such a relaxation for R|r ij | ∑ w j C j and a fully polynomial time approximation scheme to solve a relaxation of R|| ∑ w j C j . As a byproduct of our techniques we derive a polynomial time approximation scheme for the one machine scheduling problem with rejection penalties, release dates and the total weighted sum of completion times objective.
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Sviridenko, M., Wiese, A. (2013). Approximating the Configuration-LP for Minimizing Weighted Sum of Completion Times on Unrelated Machines. In: Goemans, M., Correa, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2013. Lecture Notes in Computer Science, vol 7801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36694-9_33
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DOI: https://doi.org/10.1007/978-3-642-36694-9_33
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