A 1.6 Approximation Algorithm for Routing Multiterminal Nets

The problem of connecting a set of n terminals belonging to m (signal) nets that lie on the sides of a rectangle to minimize the total area is discussed. We present an $O(n(m + \log n))$approximation algorithm to solve this problem. Our algorithm generates a solution with area $ \leqq 1.6 * {\operatorname{OPT}}$, where ${\operatorname{OPT}}$ is the area of an optimal solution. The nets are routed according to the following greedy strategy: the wire connecting all points from a net is one whose path crosses the least number of corners of the rectangle. For some nets there are several routes that cross the least number of corners. A subset of these nets is connected by wires whose paths blend with the paths for other nets. The remaining nets are routed using several strategies and $2^6 $ layouts are obtained. The best of these layouts is the solution generated by our algorithm.