A linear time optimal via assignment algorithm for Three-Dimensional channel routing

Abstract

A three-dimensional channel refers to a 3-D rectangular block with multiple routing layers. Terminals exist only on the top and the bottom layers and they form two wellaligned 2-D rectangular channels. In this paper, we consider a special version in which the three-dimensional channel contains only three layers. The routing algorithm is as follows. First, a channel routing algorithm is applied to both the top and the bottom layer to route the terminals belonging to the same net on the same layer. The second step is to form another channel routing problem as defined below. A net N is said to be an inter-layer net if it contains terminals on both the top and the bottom layers. Two via positions in the middle layer are selected for each inter-layer net N. The first via is chosen from the position immediately below one of the terminals belonging to N on the top layer, while the second is chosen from the position immediately above one of the terminals belonging to N on the bottom layer. Notice that it thus defines a channel routing problem containing only two-terminal nets in the three respective layers. The channel routing algorithm can then applied to complete the routing. In this paper, we present a linear time optimal via assignment algorithm for the second step decribed above such that number of incompletely routed nets are minimized.