Provably Good Channel Routing Algorithms

Abstract

In this paper we present three new two-layer channel routing algorithms that are provably good in that they never require more than 2d-1 horizontal tracks where d is the channel density, when each net connects just two terminals. To achieve this result, we use a slightly relaxed (but still realistic) wiring model in which wires may run on top of each other for short distances as long as they are on different layers. Two of our algorithms will never use such a “parallel run” of length greater than 2d-1 and our third algorithm will require overlap only at jog points or cross points. Since in this wiring model at least d/2 horizontal tracks are required, these algorithms produce a routing requiring no more than four times the best possible number of horizontal tracks. The second algorithm also has the property that it uses uses at most 4n contacts, where n is the number of nets being connected.