Online Multidimensional Packing Problems in the Random-Order Model

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 $Ω(d)$. Furthermore, our algorithm improves upon the best-known competitive-ratio for the online (one-dimensional) generalized assignment problem and the online knapsack problem.