Computing area and wire length efficient routes for channels

The first stage in channel routing is that of computing a routing solution S, for a given channel with as few tracks as possible. We consider a second stage in which it is desirable to reduce the total wire length without increasing area of routing. In this paper we propose efficient polynomial time algorithms for appreciably reducing the total wire length in two-, three- and multi-layer routing solutions by permuting tracks in the solution S obtained in the first stage. This results in a routing solution that is economical in terms of area as well as total wire length. Our algorithms are particularly important in practical terms since the problem of minimizing the total wire length in a routing solution is NP-hard