Approximating the Configuration-LP for minimizing weighted sum of completion times on unrelated machines

Authors:
Maxim Sviridenko;Andreas Wiese
Affiliations:
University of Warwick, UK;MPI für Informatik, Saarbrücken, Germany
Venue:
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Year:
2013

Citing 13
Cited 0

Approximation algorithms for scheduling unrelated parallel machines

Mathematical Programming: Series A and B
Fast approximation algorithms for fractional packing and covering problems

Mathematics of Operations Research
Convex quadratic and semidefinite programming relaxations in scheduling

Journal of the ACM (JACM)
Preemptive multiprocessor scheduling with rejection

Theoretical Computer Science
Scheduling Unrelated Machines by Randomized Rounding

SIAM Journal on Discrete Mathematics
Approximate Max-Min Resource Sharing for Structured Concave Optimization

SIAM Journal on Optimization
Preemptive Scheduling with Rejection

ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The Santa Claus problem

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Vehicle Routing and Staffing for Sedan Service

Transportation Science
Santa Claus schedules jobs on unrelated machines

Proceedings of the forty-third annual ACM symposium on Theory of computing
New Constructive Aspects of the Lovász Local Lemma

Journal of the ACM (JACM)
Santa claus meets hypergraph matchings

ACM Transactions on Algorithms (TALG)

Quantified Score

Hi-index	0.00

Visualization

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|rij|∑wjCj and a fully polynomial time approximation scheme to solve a relaxation of R||∑wjCj. 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.