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- W3180376268 abstract "We formalize the concept of additive approximation schemes and apply it to load balancing problems on identical machines. Additive approximation schemes compute a solution with an absolute error in the objective of at most e h for some suitable parameter h and any given e > 0. We consider the problem of assigning jobs to identical machines with respect to common load balancing objectives like makespan minimization, the Santa Claus problem (on identical machines), and the envy-minimizing Santa Claus problem. For these settings we present additive approximation schemes for h = p_{max}, the maximum processing time of the jobs.Our technical contribution is two-fold. First, we introduce a new relaxation based on integrally assigning slots to machines and fractionally assigning jobs to the slots. We refer to this relaxation as the slot-MILP. While it has a linear number of integral variables, we identify structural properties of (near-)optimal solutions, which allow us to compute those in polynomial time. The second technical contribution is a local-search algorithm which rounds any given solution to the slot-MILP, introducing an additive error on the machine loads of at most e⋅ p_{max}." @default.
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- W3180376268 date "2021-01-01" @default.
- W3180376268 modified "2023-10-03" @default.
- W3180376268 title "Additive Approximation Schemes for Load Balancing Problems" @default.
- W3180376268 doi "https://doi.org/10.4230/lipics.icalp.2021.42" @default.
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