Convex quadratic and semidefinite programming relaxations in scheduling
Journal of the ACM (JACM)
Models and Algorithms for Stochastic Online Scheduling
Mathematics of Operations Research
An R || Cmax Quantum Scheduling Algorithm
Quantum Information Processing
Approximation in preemptive stochastic online scheduling
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Stochastic Online Scheduling Revisited
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Approximability of Average Completion Time Scheduling on Unrelated Machines
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Sum edge coloring of multigraphs via configuration LP
ACM Transactions on Algorithms (TALG)
Inner product spaces for MinSum coordination mechanisms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Santa Claus schedules jobs on unrelated machines
Proceedings of the forty-third annual ACM symposium on Theory of computing
LP-based online scheduling: from single to parallel machines
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
List scheduling in order of α-points on a single machine
Efficient Approximation and Online Algorithms
Efficient algorithms for average completion time scheduling
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
On-line scheduling to minimize average completion time revisited
Operations Research Letters
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Coordination mechanisms from (almost) all scheduling policies
Proceedings of the 5th conference on Innovations in theoretical computer science
Computers and Operations Research
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We present a new class of randomized approximation algorithms for unrelated parallel machine scheduling problems with the average weighted completion time objective. The key idea is to assign jobs randomly to machines with probabilities derived from an optimal solution to a linear programming (LP) relaxation in time-indexed variables. Our main results are a $(2+\varepsilon)$-approximation algorithm for the model with individual job release dates and a $(3/2+\varepsilon)$-approximation algorithm if all jobs are released simultaneously. We obtain corresponding bounds on the quality of the LP relaxation. It is an interesting implication for identical parallel machine scheduling that jobs are randomly assigned to machines, in which each machine is equally likely. In addition, in this case the algorithm has running time O(n log n) and performance guarantee 2. Moreover, the approximation result for identical parallel machine scheduling applies to the on-line setting in which jobs arrive over time as well, with no difference in performance guarantee.