An optimal channel-routing algorithm in the times square model

Channel routing is an important, time-consuming, and difficult problem in VLSI layout design, In this paper, we consider the two-terminal channel routing problem in the new routing model, called times square model (TSM); see, Lodj, Info. Proc. Lett., vol. 35, p. 41, 1990.; where the grid is composed of horizontal tracks, right tracks (with slope +60/spl deg/) and left tracks (with slope -60/spl deg/). We show a new lower bound [2d/3]-1 to the width of channel and present an optimal algorithm for two-terminal channel routing problems, which obtains [2d/3]+2 as an upper bound to the channel width where d is the channel density. The algorithm not only utilizes the horizontal tracks, but also the zig-zag connections, thus achieving the routing optimality.>