Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Theoretical Computer Science
Improved approximation schemes for scheduling unrelated parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
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Convex programming for scheduling unrelated parallel machines
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Approximation Algorithms for Scheduling on Multiple Machines
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
Theoretical Computer Science
An approximation algorithm for max-min fair allocation of indivisible goods
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An optimal rounding gives a better approximation for scheduling unrelated machines
Operations Research Letters
Santa Claus Meets Hypergraph Matchings
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Information Processing Letters
MaxMin allocation via degree lower-bounded arborescences
Proceedings of the forty-first annual ACM symposium on Theory of computing
A note on graph balancing problems with restrictions
Information Processing Letters
Santa Claus schedules jobs on unrelated machines
Proceedings of the forty-third annual ACM symposium on Theory of computing
On the configuration-LP for scheduling on unrelated machines
ESA'11 Proceedings of the 19th European conference on Algorithms
Santa claus meets hypergraph matchings
ACM Transactions on Algorithms (TALG)
Parallel machine scheduling with nested job assignment restrictions
Operations Research Letters
Assigning sporadic tasks to unrelated parallel machines
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The 2-valued case of makespan minimization with assignment constraints
Information Processing Letters
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 design a 1.75-approximation algorithm for a special case of scheduling parallel machines to minimize the makespan, namely the case where each job can be assigned to at most two machines with the same processing time on either machine. (This is a special case of so-called restricted assignment, where the set of eligible machines can be arbitrary for each job.) We also show that even for this special case it is NP-hart to compute better than 1.5 approximation. This is the first improvement of the approximation ratio 2 of Lenstra, Shmoys, and Tardos [Approximation algorithms for scheduling unrelated parallel machines, Math. Program. 46:259--271, 1990], for any special case with unbounded number of machines. Our lower bound yields the same ratio as their bound which works for restricted assignment, and which is still the state-of-the-art lower bound even for the most general case.