Algorithms for routing around a rectangle

Simple efficient algorithms are given for three routing problems around a rectangle. The algorithms find routing in two or three layers for two-terminal nets specified on the sides of a rectangle. All algorithms run in linear time. One of the three routing problems is the minimum area routing previously considered by LaPaugh and Gonzalez and Lee. The algorithms they developed run in time O(n³) and O(n) respectively. The present simple linear time algorithm is based on a theorem of Okamura and Seymour and on a data structure developed by Suzuki, Ishiguro and Nishizeki.