Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
The boundaries of submodular functions
Computational Mathematics and Mathematical Physics
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
Operations Research Letters
Partially ordered knapsack and applications to scheduling
Discrete Applied Mathematics
Single machine precedence constrained scheduling is a vertex cover problem
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Scheduling with Precedence Constraints of Low Fractional Dimension
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On the Approximability of Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Approximating precedence-constrained single machine scheduling by coloring
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
A 2-approximation algorithm for the network substitution problem
Operations Research Letters
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We study the problem of scheduling a single machine with the precedence relation on the set of jobs to minimize average weighted completion time. The problem is strongly NP-hard. The first combinatorial 2-approximation algorithm for this scheduling problem was developed by the author in 1992 (in fact, this algorithm solves a more general problem). Here we give an efficient implementation of this algorithm and show that its running time is O(nMF(n,m)), where n is the number of jobs, m is the number of arcs in the precedence relation graph, and MF(n,m) denotes the complexity of the maximal flow computation in a network with n nodes and m arcs. Thus, our algorithm is competitive to the best 2-approximation algorithms for this scheduling problem developed starting since 1997.