Congestion Reduction in Traditional and New Routing Architectures

In dense integrated circuit designs, management of routing congestion is essential; an over congested design may be unroutable. Many factors influence congestion: placement, routing, and routing architecture all contribute. Previous work has shown that different placement tools can have substantially different demands for each routing layer; our objective is to develop methods that allow “tuning” of interconnect topologies to match routing resources. We focus on congestion minimization for both Manhattan and non-Manhattan routing architectures, and have two main contributions. First, we combine prior heuristics for non-Manhattan Steiner trees and Preferred Direction Steiner trees into a hybrid approach that can handle arbitrary routing directions, via minimization, and layer assignment of edges simultaneously. Second, we present an effective method to adjust Steiner tree topologies to match routing demand to resource, resulting in lower congestion and better routability

Hardness and Approximation of Octilinear Steiner Trees

Given a point set K of terminals in the plane, the octilinear Steiner tree problem is to find a shortest tree that interconnects all terminals and edges run either in horizontal, vertical, or 45° diagonal direction. This problem is fundamental for the novel octilinear routing paradigm in VLSI design, the so-called X-architecture. As the related rectilinear and the Euclidian Steiner tree problem are well-known to be NP-hard, the same was widely believed for the octilinear Steiner tree problem but left open for quite some time. In this paper, we prove the NP-completeness of the decision version of the octilinear Steiner tree problem. We also show how to reduce the octilinear Steiner tree problem to the Steiner tree problem in graphs of polynomial size with the following approximation guarantee. We construct a graph of size O(n^2/epsilon^2) which contains a (1+epsilon)-approximation of a minimum octilinear Steiner tree for every epsilon > 0 and n = |K|. Hence, we can apply any k-approximation algorithm for the Steiner tree problem in graphs (the currently best known bound is k=1.55) and achieve an (k+epsilon)-approximation bound for the octilinear Steiner tree problem. This approximation guarantee also holds for the more difficult case where the Steiner tree has to avoid blockages (obstacles bounded by octilinear polygons)

An Exact Algorithm for the Uniformly-Oriented Steiner Tree Problem

An exact algorithm to solve the Steiner tree problem for uniform orientation metrics in the plane is presented. The algorithm is based on the two-phase model, consisting of full Steiner tree (FST) generation and concatenation, which has proven to be very successful for the rectilinear and Euclidean Steiner tree problems. By applying a powerful canonical form for the FSTs, the set of optimal solutions is reduced considerably