Approximation Schemes for Covering and Scheduling on Related Machines
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
A polynomial-time approximation scheme for maximizing the minimum machine completion time
Operations Research Letters
Maximizing the Minimum Load: The Cost of Selfishness
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Max-min online allocations with a reordering buffer
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Optimal semi-online scheduling algorithms on a small number of machines
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
The cost of selfishness for maximizing the minimum load on uniformly related machines
Journal of Combinatorial Optimization
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In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs. We present a deterministic algorithm with competitive ratio 11/6≤ 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24≥ 1.791.