To Close Is Easier Than To Open: Dual Parameterization To k-Median.

The \(k\)-Median problem is one of the well-known optimization problems that formalize the task of data clustering. Here, we are given sets of facilities F and clients C, and the goal is to open k facilities from the set F, which provides the best division into clusters, that is, the sum of distances from each client to the closest open facility is minimized. In the Capacitated \(k\) -Median, the facilities are also assigned capacities specifying how many clients can be served by each facility.