Online models that allow recourse are highly effective in situations where classical models are too pessimistic. One such problem is the online machine covering problem on identical machines. In this setting jobs arrive one by one and must be assigned to machines with the objective of maximizing the minimum machine load. When a job arrives, we are allowed to reassign some jobs as long as their total size is (at most) proportional to the processing time of the arriving job. The proportionality constant is called the migration factor of the algorithm. #R##N#Using a new rounding procedure specially tailored for online problems, we design a $(4/3+\varepsilon)$-competitive algorithm using migration factor $\tilde{O}(1/\varepsilon^3)$. At every arrival we run an adaptation of the Largest Processing Time first (LPT) algorithm. Since the new job can cause a complete change of the assignment of smaller jobs, a low migration factor is achieved by carefully exploiting the highly symmetric structure obtained by our rounding. #R##N#We also study local search algorithms for the machine covering problem, and show that jump and swap optimality have an approximation ratio which lies in the interval $[1.691, 1.75]$ and can be adapted to the online context with a small constant as migration factor. Our lower bound is obtained by a nice construction based on Sylvester's sequence.
['Waldo Gálvez', 'José A. Soto', 'José Verschae']
Symmetry exploitation for Online Machine Covering with Bounded Migration