Finding Maximum Disjoint Set of Boundary Rectangles With Application to PCB Routing.

Motivated by the bus escape routing problem in printed circuit boards (PCBs), we study the following optimization problem: given a set of rectangles attached to the boundary of a rectangular region, find a subset of nonoverlapping rectangles with maximum total weight. We present an efficient algorithm that solves this problem optimally in ${O(n^{4})}$ time, where ${n}$ is the number of rectangles in the input instance. This improves over the best previous ${O(n^{6})}$ -time algorithm available for the problem. We also present two efficient approximation algorithms for the problem that find near-optimal solutions with guaranteed approximation factors. The first algorithm finds a 2-approximate solution in ${O(n^{2})}$ time, and the second one computes a ${4/3}$ -approximation in ${O(n^{3})}$ time. The experimental results demonstrate the efficiency of both our exact and approximation algorithms.