Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Scheduling unrelated machines with costs
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Approximation algorithms
Improved Approximation Schemes for Scheduling Unrelated Parallel Machines
Mathematics of Operations Research
Scheduling Unrelated Machines by Randomized Rounding
SIAM Journal on Discrete Mathematics
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On allocations that maximize fairness
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Graph balancing: a special case of scheduling unrelated parallel machines
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Santa Claus Meets Hypergraph Matchings
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
MaxMin allocation via degree lower-bounded arborescences
Proceedings of the forty-first annual ACM symposium on Theory of computing
On Allocating Goods to Maximize Fairness
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
New Constructive Aspects of the Lovasz Local Lemma
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods
SIAM Journal on Computing
An optimal rounding gives a better approximation for scheduling unrelated machines
Operations Research Letters
On the configuration-LP for scheduling on unrelated machines
ESA'11 Proceedings of the 19th European conference on Algorithms
Assigning sporadic tasks to unrelated parallel machines
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Quasi-polynomial local search for restricted max-min fair allocation
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
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines, i.e., job j requires time pij if processed on machine i. More than two decades after its introduction it is still the algorithm of choice even in the restricted model where processing times are of the form pij ∈ pj, ∞. This problem, also known as the restricted assignment problem, is NP-hard to approximate within a factor less than 1.5 which is also the best known lower bound for the general version. Our main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor 33/17 + ε ~ 1.9412 + ε, where ε 0 is an arbitrarily small constant. The result is obtained by upper bounding the integrality gap of a certain strong linear program, known as configuration LP, that was previously successfully used for the related Santa Claus problem. Similar to the strongest analysis for that problem our proof is based on a local search algorithm that will eventually find a schedule of the mentioned approximation guarantee, but is not known to converge in polynomial time.