# Moving points to reach linear separability

Let R be a set of red points and B a set of blue points in d-dimensional space. Assume that all the points are in general position and that R and B are no line separable. We want to compute the minimum effort necessary to move the points till the sets R and B become line separable. In order to measure the effort, the following criteria can be handled:

1. Minimizing the maximum distance of those points that have to be moved till R and B become line separable: MinMax criterium.
2. Minimizing the sum of distances of those points that have to be moved till R and B become line separable: MinSum criterium.
3. Minimizing the sum of the squared distances of those points that have to be moved till R and B become line separable: MinSum squared criterium.

Thus our moving separability problem is to design good algorithms which computes the minimum effort (measured by any of the above criteria) necessary to get the linear separability. We are still working on the dynamic version of our moving separability problem. Instead of having static red and blue points that have to be moved, the red and blue points are moving along some known rectilinear trajectories with constant velocities which can be all equal or different. In this scenario we want to determine the instant in which the effort to get the linear separability is minimum by using any of the three criteria above described. In this sense we shall talk about static or dynamic moving separability problems.

This is joint work with Delia Garijo, David Rappaport and Jorge Urrutia