A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Single-machine scheduling polyhedra with precedence constraints
Mathematics of Operations Research
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
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On the approximability of average completion time scheduling under precedence constraints
Discrete Applied Mathematics
Optimal Long Code Test with One Free Bit
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Operations Research Letters
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We consider the problem of minimizing the weighted sum of completion times on a single machine subject to bipartite precedence constraints in which all minimal jobs have unit processing time and zero weight, and all maximal jobs have zero processing time and unit weight. For various probability distributions over these instances---including the uniform distribution---we show several “almost all”-type results. First, we show that almost all instances are prime with respect to a well-studied decomposition for this scheduling problem. Second, we show that for almost all instances, every feasible schedule is arbitrarily close to optimal. Finally, for almost all instances, we give a lower bound on the integrality gap of various linear programming relaxations of this problem.