Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A survey of approximately optimal solutions to some covering and packing problems
ACM Computing Surveys (CSUR)
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
Two-Dimensional Gantt Charts and a Scheduling Algorithm of Lawler
SIAM Journal on Discrete Mathematics
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Partially-Ordered Knapsack and Applications to Scheduling
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
On the approximability of average completion time scheduling under precedence constraints
Discrete Applied Mathematics
Operations Research Letters
Scheduling with Precedence Constraints of Low Fractional Dimension
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A better approximation ratio for the vertex cover problem
ACM Transactions on Algorithms (TALG)
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
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
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In this paper we study the single machine precedence constrained scheduling problem of minimizing the sum of weighted completion time. Specifically, we settle an open problem first raised by Chudak & Hochbaum and whose answer was subsequently conjectured by Correa & Schulz. The most significant implication of our result is that the addressed scheduling problem is a special case of the vertex cover problem. This will hopefully be an important step towards proving that the two problems behave identically in terms of approximability. As a consequence of our result, previous results for the scheduling problem can be explained, and in some cases improved, by means of vertex cover theory. For example, our result implies the existence of a polynomial time algorithm for the special case of two-dimensional partial orders. This considerably extends Lawler's result from 1978 for series-parallel orders.