The Container Selection Problem

We introduce and study a network resource management problem that is a special case of nonmetric k-median, naturally arising in cross platform scheduling and cloud computing. In the continuous d-dimensional container selection problem, we are given a set C ⊂ Rd of input points, for some d ≥ 2, and a budget k. An input point p can be assigned to a “container point” c only if c dominates p in every dimension. The assignment cost is then equal to the 1-norm of the container point. The goal is to find k container points in Rd , such that the total assignment cost for all input points is minimized. The discrete variant of the problem has one key distinction, namely, the container points must be chosen from a given set F of points. For the continuous version, we obtain a polynomial time approximation scheme for any fixed dimension d ≥ 2. On the negative side, we show that the problem is NP-hard for any d ≥ 3. We further show that the discrete version is significantly harder, ...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Viswanath Nagarajan, Kanthi K. Sarpatwar, Baruch Schieber, Hadas Shachnai, Joel L. Wolf
• Keywords: Algorithms, APPROX 2015