A Faster One-Dimensional Topological Compaction Algorithm with Jog Insertion

Abstract

We consider the problem of one-dimensional topological compaction with jog insertions. By combining both geometric and graph-theoretic approaches we present a faster and simpler algorithm to improve over previous results. The compaction algorithm takes as input a sketch consisting of a set F of features and a set W of wires, and minimizes the horizontal width of the sketch while maintaining its routability. The algorithm consists of the following steps: constructing a horizontal constraint graph, computing all possible jog positions, computing the critical path, relocating the features, and reconstructing a new sketch homotopic to the input sketch, which is suitable for detailed routing. The algorithm runs in O(|F| ⋅ |W|) worst-case time and space, which is asymptotically optimal in the worst case. Experimental results are also presented.