In the "Covering Things with Things" paper from Langerman and Morin, they mention the BST-Dim-Set-Cover, which is a FPT algorithm for point-line-cover, at page 666.
The algorithm chooses each point p from a set S and then subdivides it into k-lines.
This can be seen as a special case of set cover. All points (each p belongs to P) are in a cartesian plane, and the algorithm needs to find if they can be covered by k lines (where each line l belongs to L). This image below clarifies it further:
My question is around what is written in the paper linked above at page 666 regarding where is p taken from: At some point during the text it says "Otherwise, the algorithm chooses an element p ∈ S'". However, further down in the algorithm it says "choose p ∈ S" (without the prime symbol).
Is p taken from S or S' (S prime)?