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.