Randomized approximation algorithms in combinatorial optimization
Approximation algorithms for NP-hard problems
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Scheduling to minimize average completion time: off-line and on-line algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorthims for scheduling with release dates
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Optimal scheduling of multiclass parallel machines
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Discrete Mathematics
Non-approximability Results for Scheduling Problems with Minsum Criteria
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
Scheduling-LPs Bear Probabilities: Randomized Approximations for Min-Sum Criteria
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Semidefinite Relaxations for Parallel Machine Scheduling
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
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
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In network scheduling a set of jobs must be scheduled on unrelated parallel processors or machines which are connected by a network. Initially, each job is located on some machine in the network and cannot be started on another machine until sufficient time elapses to allow the job to be transmitted there. This setting has applications, e. g., in distributed multi-processor computing environments and also in operations research; it can be modeled by a standard parallel machine environment with machine-dependent release dates.We consider the objective of minimizing the total weighted completion time.The main contribution of this paper is a provably good convex quadratic programming relaxation of strongly polynomial size for this problem. Until now, only linear programming relaxations in time- or interval-indexed variables have been studied. Those LP relaxations, however, suffer from a huge number of variables. In particular, the best previously known relaxation is of exponential size and can therefore not be solved exactly in polynomial time. As a result of the convex quadratic programming approach we can give a very simple and easy to analyze randomized 2-approximation algorithm which slightly improves upon the best previously known approximation result. Furthermore, we consider preemptive variants of network scheduling and derive approximation results and results on the power of preemption which improve upon the best previously known results for these settings.