Online Multidimensional Packing Problems in the Random-Order Model

Authors David Naori, Danny Raz

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David Naori
  • Computer Science Department, Technion, 32000 Haifa, Israel
Danny Raz
  • Computer Science Department, Technion, 32000 Haifa, Israel

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David Naori and Danny Raz. Online Multidimensional Packing Problems in the Random-Order Model. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We study online multidimensional variants of the generalized assignment problem which are used to model prominent real-world applications, such as the assignment of virtual machines with multiple resource requirements to physical infrastructure in cloud computing. These problems can be seen as an extension of the well known secretary problem and thus the standard online worst-case model cannot provide any performance guarantee. The prevailing model in this case is the random-order model, which provides a useful realistic and robust alternative. Using this model, we study the d-dimensional generalized assignment problem, where we introduce a novel technique that achieves an O(d)-competitive algorithms and prove a matching lower bound of Omega(d). Furthermore, our algorithm improves upon the best-known competitive-ratio for the online (one-dimensional) generalized assignment problem and the online knapsack problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Theory of computation → Online algorithms
  • Random Order
  • Generalized Assignment Problem
  • Knapsack Problem
  • Multidimensional Packing
  • Secretary Problem


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