Four-bend top-down global routing

We propose a new global net distribution approach for high-performance m×m two-dimensional arrays of very large scale integration and multichip-modules. The objective is to route n nets with minimum density of global cells, using a “small” number of bends. There are a number of applications where it is necessary to limit the number of bends on each wire. For example, it is desirable to limit the number of bends on each microstrip (transmission) line, for mismatches of line impedance can cause reflections from the junction points such as bends and vias. Furthermore, for high-performance routing, intersections of wires cause the use of more vias, which in turn require the use of more routing resources (because of the larger via pitch). This is the first paper that addresses a graph-theoretic framework to solve the bend-constrained global routing problem in two-dimensional arrays. In this paper, at each level of an underlying quad-tree, we present a novel four-bend routing algorithm by decomposing the original problem at level i into two subproblems that can be solved exactly based on a two-stage approach of smaller-sized linear program followed by min-cost flow networks. The overall (i.e., entire level of the four-way partition hierarchy) constraint and variable size for the first stage is O(md_o), while the overall run time for the second stage is O(n³ log n²). The time complexity of such a hierarchical approach is one order of magnitude less than one of constructing a global routing using the min-cost-flow-based flat design approach. Last, we present an extension that permits a limited degree of control over the number of bends. The proposed algorithm can also be used for estimating the wireability in the early design planning stage for high-level synthesis. Experimental results showed the effectiveness of the proposed algorithm