Short wire routing in convex grids

Abstract

Knock-knee routing of two-terminal nets is mathematically modelled and successfully solved in a lot of settings by multicommodity-flow techniques. The primary goal of routing, the fast construction of a solution whenever it exists at all, is thus well understood and controlled.

A major drawback of these provably good algorithms is that they fail to reach any of the secondary optimization criteria, wire length and number of bends. We identify a major reason for this and suggest an empirically very successful way to overcome this fundamental weakness in case of a rather general shape of the routing region, the convex grids.

The resulting new algorithm shares the good properties of the old one, it solves whenever it is possible and is as efficient.

Part of this research was done while the authors were with Lehrstuhl für angewandte Mathematik insbesondere Informatik, Rheinisch-Westfälische Technische Hochschule Aachen