Routing through a Rectangle

Abstract

In this paper an O(N log N) algorithm for routing through a rectangle is presented. Consider an n-by-m rectangular grid and a set of N two-terminal nets. A net is a pair of points on the boundary of the rectangle. A layout is a set of edge-disjoint paths, one for each net. Our algorithm constructs a layout, if there is one, in O(N log N) time; this contrasts favorably with the area of the layout that might be as large as N2. The layout constructed can be wired using four layers of interconnect with only O(N) contact cuts. A partial extension to multiterminal nets is also discussed. © 1986, ACM. All rights reserved.