Merging two partial (jointly overdetermined) sets of ordering information

Question

I have a web app with data in a grid. The user can reorder the columns, and the server can change which columns exist. I would like to save the user\'s column order in a coo

Answer 1

One definition that might be reasonable is to minimize the number of inversions relative to the server's order, subject to the constraint that the restriction to the columns in common of the two orders be equal. I don't know offhand an algorithm to minimize this objective.