Abstract: A geometric model is considered for the problem of minimizing access control lists (ACLs) in network routers. A colored rectilinear pattern is created within an initially white rectangular canvas, and the basic operation is to choose a subrectangle and paint it a single color, overwriting all previous colors in the rectangle. The method operates on rectangular rule lists (RRLs) and access control lists (ACLs) in which all rectangles are strips that extend either the full length or the full height of the canvas. A polynomial-time algorithm optimally constructs such patterns when, as in the ACL application, the only colors are black and white (permit or deny). That algorithm is complemented by a significantly faster approximation algorithm that is guaranteed to be no worse than 3/2 optimal.