Approximability of Average Completion Time Scheduling on Unrelated Machines
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Improved Bounds for Flow Shop Scheduling
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
Hardness of Approximating Flow and Job Shop Scheduling Problems
Journal of the ACM (JACM)
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
Bounding the running time of algorithms for scheduling and packing problems
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless , none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by APX-hardness proofs.We show that, whereas scheduling on unrelated machines with unit weights is polynomially solvable, the problem becomes APX-hard if release dates or weights are added. We further show APX-hardness for scheduling in flow shops, job shops, and open shops. We also investigate the problems of scheduling on parallel machines with precedence constraints and unit processing times, and two variants of the latter problem with unit communication delays; for these problems we provide lower bounds on the worst-case behavior of any polynomial-time approximation algorithm through the gap-reduction technique.