Approximation results for a bicriteria job scheduling problem on a single machine without preemption
Information Processing Letters
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Discrete Applied Mathematics
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
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
Approximating Single Machine Scheduling with Scenarios
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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
Approximation results for a bicriteria job scheduling problem on a single machine without preemption
Information Processing Letters
Conditional hardness of precedence constrained scheduling on identical machines
Proceedings of the forty-second ACM symposium on Theory of computing
A constant factor approximation algorithm for generalized min-sum set cover
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Mathematics of Operations Research
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
Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
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
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
List scheduling in order of α-points on a single machine
Efficient Approximation and Online Algorithms
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
Approximation algorithms for scheduling problems with a modified total weighted tardiness objective
Operations Research Letters
Asymptotically optimal schedules for single-server flow shop problems with setup costs and times
Operations Research Letters
Vertex cover in graphs with locally few colors
Information and Computation
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We present an in-depth theoretical, algorithmic, and computational study of a linear programming (LP) relaxation to the precedence constrained single-machine scheduling problem 1|prec|S jw jC jto minimize a weighted sum of job completion times. On the theoretical side, we study the structure of tight parallel inequalities in theLP relaxation and show thatevery permutation schedule that is consistent with Sidney's decomposition has total cost no more than twice the optimum. On the algorithmic side, we provide a parametric extension to Sidney's decomposition and show that a finest decomposition can be obtained by essentially solving a parametric minimum-cut problem. Finally, we report results obtained by an algorithm based on these developments on randomly generated instances with up to 2,000 jobs.