An algorithm for finding a non-trivial lower bound for channel routing

Channel routing is a key problem in the physical design of VLSI chips. It is known that max(d_max,v_max) is a lower bound on the number of tracks required in the reserved two-layer Manhattan routing model, where d_max is the channel density and v_max is the length of the longest path in the vertical constraint graph. In this paper we propose a polynomial time algorithm that computes a better and non-trivial lower bound on the number of trades required for routing a channel without doglegging. This algorithm is also applicable for computing a lower bound on the number of tracks in the three-layer no-dogleg HVH routing as well as two- and three-layer restricted dogleg routing models