Faster compression of patterns to Rectangle Rule Lists

Abstract

Access Control Lists (ACLs) are an essential security component in network routers. ACLs can be geometrically modeled as a two-dimensional black and white grid; our interest is in the most efficient way to represent such a grid. The more general problem is that of Rectangle Rule Lists (RRLs) minimization, which is finding the least number of rectangles needed to generate a given pattern. The scope of this paper focuses on a restricted version of RRLs minimization in which only rectangles that span the length or width of the grid are considered. Applegate et al.'s paper “Compressing Rectilinear Pictures and Minimizing Access Control Lists” gives an algorithm for finding an optimal solution for strip-rule RRLs minimization in O(n3) time, where n is the total number of rows and columns in the grid. Following the structure of Applegate et al.'s algorithm, we simplify the solution, remove redundancies in data structures, and exploit overlapping sub-problems in order to achieve an optimal solution for strip-rule RRLs minimization in O(n2 log n) time.