Symmetry Exploitation for Online Machine Covering with Bounded Migration
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.
By rounding the processing times, which yields useful structural properties for online packing and covering problems, we design first a simple (1.7 + epsilon)-competitive algorithm using a migration factor of O(1/epsilon) which maintains at every arrival a locally optimal solution with respect to the Jump neighborhood. After that, we present as our main contribution a more involved (4/3+epsilon)-competitive algorithm using a migration factor of O~(1/epsilon^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 in both cases, a low migration factor is achieved by carefully exploiting the highly symmetric structure obtained by the rounding procedure.
Machine Covering
Bounded Migration
Online
Scheduling
LPT
Theory of computation~Scheduling algorithms
Theory of computation~Online algorithms
32:1-32:14
Regular Paper
This work was partially supported by SNSF Grant APXNET 200021_159697/1 and CONICYT-Chile through projects FONDECYT 1181527 and 1181180, PCI PII 20150140 and PIA AFB170001.
https://arxiv.org/abs/1612.01829
Waldo
Gálvez
Waldo Gálvez
IDSIA, USI-SUPSI, Lugano, Switzerland
José A.
Soto
José A. Soto
Departamento de Ingeniería Matemática & CMM, Universidad de Chile, Santiago, Chile
José
Verschae
José Verschae
Facultad de Matemáticas & Escuela de Ingeniería, Pontificia Universidad Católica de Chile, Santiago, Chile
10.4230/LIPIcs.ESA.2018.32
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Waldo Gálvez, José A. Soto, and José Verschae
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