A PTAS for minimizing the weighted sum of job completion times on parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Optimal stochastic scheduling in multiclass parallel queues
SIGMETRICS '99 Proceedings of the 1999 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Algorithms Based on Randomization and Linear and Semidefinite Programming
SOFSEM '98 Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Convex Quadratic Programming Relaxations for Network Scheduling Problems
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Designing PTASs for MIN-SUM Scheduling Problems
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
An approximation algorithm for scheduling two parallel machines with capacity constraints
Discrete Applied Mathematics
Designing PTASs for MIN-SUM scheduling problems
Discrete Applied Mathematics - Special issue: Efficient algorithms
Designing PTASs for MIN-SUM scheduling problems
Discrete Applied Mathematics - Special issue: Efficient algorithms
A 32-approximation algorithm for parallel machine scheduling with controllable processing times
Operations Research Letters
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We consider the problem of scheduling unrelated parallel machines so as to minimize the total weighted completion time of jobs. Whereas the best previously known approximation algorithms for this problem are based on LP relaxations, we give a $3/2$--approximation algorithm that relies on a convex quadratic programming relaxation. For the special case of two machines we present a further improvement to a $1.2752$--approximation; we introduce a more sophisticated semidefinite programming relaxation and apply the random hyperplane technique introduced by Goemans and Williamson for the MaxCut problem and its refined version of Feige and Goemans. To the best of our knowledge, this is the first time that convex and semidefinite programming techniques (apart from LPs) are used in the area of scheduling.