A Graph Theoretic Approach to Feed-Through Pin Assignment

We study in this paper the feed-through pin assignment problem for cell based design that assigns global nets to feed-through cells or implicit feed-through ports. On a single row, for a restricted permutation of global nets, we develop a graph theoretic approach for optimally minimizing the density of the channel above (below) the row subject to the bound on the density of the channel below (above) the row. Based on this technique, an approach for iteratively improving multiple row feed-through pin assignment can be developed. We show that our approach is also aplicable to the design style in which there is an over-the-cell feed-through layer. I. Introduction Feed-through assignment is a necessary process in standard-cell layout. After the global route for each net is determined by a global router, on each cell row we need to assign feed-through ports to all the nets that cross the row (feed-through nets). Detailed routing will then be performed by a channel router. Since channel density is an accurate estimation of the number of routing tracks required for each channel, the main objective of feed-through assignment is to minimize the total density of all channels. Recently, there are many good research works on feed-through assignment problem 1, 2, 3]. All these approaches assume the feed-through ports reserved for feed-through nets are determined and xed. In this paper, we assume that there are two types of feed-through ports-implicit feed-through ports in ordinary cells and feed-through cells. We propose an approach for improving single row feed-through assignment which has the advantage that the position of feed-through ports need not to be xed. There are several features in our approach. First, all cells on each row can be shifted as long as the row length does not exceed the given maximum length. Second, there can be zero or more feed-through cells (if necessary) between each pair of adjacent ordinary cells. Third, the size of the set of feed-through nets may be reduced by merging equivalent nets. We model the problem of single-row feed-through assignment as a graph problem. We construct a directed acyclic graph, such that each vertex corresponds to a feed-through cell, an implicit feed-through port, or an ordinary cell, and each edge corresponds to a segment of the cell row. The edge weights are ordered-pairs which store the density of the sub-channel above and below the segment. We develop an eecient optimal single-row feed-through assignment …