Conditional hardness of precedence constrained scheduling on identical machines
Proceedings of the forty-second ACM symposium on Theory of computing
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On the Approximability of Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Hardness of Precedence Constrained Scheduling on Identical Machines
SIAM Journal on Computing
The feedback arc set problem with triangle inequality is a vertex cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
Vertex cover in graphs with locally few colors
Information and Computation
| Hi-index | 0.00 |
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 and Hochbaum and whose answer was subsequently conjectured by Correa and Schulz. As shown by Correa and Schulz, the proof of this conjecture implies that the addressed scheduling problem is a special case of the vertex cover problem. This means that previous results for the scheduling problem can be explained, and in some cases improved, by means of vertex cover theory. For example, the conjecture 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.