Symmetry Exploitation for Online Machine Covering with Bounded Migration

Authors Waldo Gálvez, José A. Soto, José Verschae

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Author Details

Waldo Gálvez
  • IDSIA, USI-SUPSI, Lugano, Switzerland
José A. Soto
  • Departamento de Ingeniería Matemática & CMM, Universidad de Chile, Santiago, Chile
José Verschae
  • Facultad de Matemáticas & Escuela de Ingeniería, Pontificia Universidad Católica de Chile, Santiago, Chile

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Waldo Gálvez, José A. Soto, and José Verschae. Symmetry Exploitation for Online Machine Covering with Bounded Migration. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
  • Theory of computation → Online algorithms
  • Machine Covering
  • Bounded Migration
  • Online
  • Scheduling
  • LPT


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