Routing through a rectangle

Abstract

In this paper we present an O(Nlog N) algorithm for routing through a rectangle. 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 time O(NlogN) which contrasts favorably to the area of the layout which might be as large as N^{2}. The layout constructed can be wired using 4 layers of interconnect with only O(N) contact-cuts. A partial extension to multi-terminal nets is also discussed.