Exact routing with search space reduction

The layout problem in VLSI-design can be broken up into the subtasks partitioning, floorplanning, placement, and routing: In the routing phase, a large number of connections between the blocks and cells have to be established, while intersections lead to short circuits and, therefore, have to be avoided. We present an approach for exact routing of multiterminal nets that complements traditional routing techniques. It is particularly well suited for an application to dense problem instances and the completion of routing in subregions, which turn out to be difficult for routing tools based on heuristic methods. The exact router proposed uses symbolic methods, i.e., MDDs (Multivalued Decision Diagrams) for representation of the routing space. For the necessary computations of routing solutions, we profit considerably from the efficient basic operations on MDDs. All possible solutions to the routing problem are represented by one single MDD and, once this MDD is given, routability can be decided within constant time. To reduce the search space of possible routing solutions, so-called forced cells are computed. Experimental results are given to show the feasibility and the practicability of the approach.