The first stage of over-the-cell routing in the horizontally connected vertically connected (HCVC) model is formulated as follows: Given two rows of terminals, find a planar routing to connect a subset of nets (with weights) on each row of terminals using a f i e d number of tracks to maximize the total weight. This problem is called the two row fixed height planar routing (TFPR) problem [CPL93]. The complexity of the TFPR problem was unknown up to now. An approximation algorithm for the TFPR problem was presented in [CPL93]. In this paper we present a O(nZ * h2) time algorithm to solve the TFPR problem optimally, where n is the number of terminals and h is the height of the standard cells. Our algorithm can be used to improve the perjormance of several over-the-cell channel routers including the ones in [CPL93] and [HSS93]. ' Dept. of Computer Science, The UNv. of Texas at Dallas, Richardson, TX 75083-0688 xliu@utdallas.edu, tollis@utdallas.eduthe over-the-cell region is divided into two parts vertically by the power/ground busses in the middle of the cell.