eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-02
42:1
42:17
10.4230/LIPIcs.ICALP.2021.42
article
Additive Approximation Schemes for Load Balancing Problems
Buchem, Moritz
1
Rohwedder, Lars
2
Vredeveld, Tjark
1
Wiese, Andreas
3
Maastricht University, Maastricht, The Netherlands
EPFL, Lausanne, Switzerland
University of Chile, Santiago, Chile
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 ε h for some suitable parameter h and any given ε > 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 ε⋅ p_{max}.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol198-icalp2021/LIPIcs.ICALP.2021.42/LIPIcs.ICALP.2021.42.pdf
Load balancing
Approximation schemes
Parallel machine scheduling