Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming
Journal of the ACM (JACM)
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
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
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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
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
A note on graph balancing problems with restrictions
Information Processing Letters
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
Santa Claus schedules jobs on unrelated machines
Proceedings of the forty-third annual ACM symposium on Theory of computing
Bin packing via discrepancy of permutations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An optimal rounding gives a better approximation for scheduling unrelated machines
Operations Research Letters
The 2-valued case of makespan minimization with assignment constraints
Information Processing Letters
RETRAiN: a REcommendation tool for reconfiguration of retail bank branch
ICSOC'12 Proceedings of the 10th international conference on Service-Oriented Computing
Partitioned EDF scheduling on a few types of unrelated multiprocessors
Real-Time Systems
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Closing the approximability gap between 3/2 and 2 for the minimum makespan problem on unrelated machines is one of the most important open questions in scheduling. Almost all known approximation algorithms for the problem are based on linear programs (LPs). In this paper, we identify a surprisingly simple class of instances which constitute the core difficulty for LPs: the so far hardly studied unrelated graph balancing case in which each job can be assigned to at most two machines. We prove that already for this basic setting the strongest known LP-formulation - the configuration-LP - has an integrality gap of 2, matching the best known approximation factor for the general case. This points towards an interesting direction of future research. The result is shown by a sophisticated construction of instances, based on deep insights on two key weaknesses of the configuration-LP. For the objective of maximizing the minimum machine load in the unrelated graph balancing setting we present an elegant purely combinatorial 2-approximation algorithm with only quadratic running time. Our algorithm uses a novel preprocessing routine that estimates the optimal value as good as the configuration-LP. This improves on the computationally costly LP-based (2 + ε)-approximation algorithm by Chakrabarty et al. [6].