Two-dimensional compaction for placement refinement

A two-dimensional compaction algorithm is presented which is developed primarily for placement refinement of a building-block layout. For a given placement, a mixed-adjacency graph is derived and then a set of graph operations are applied to the graph to accomplish two-dimensional compaction. The placement can be updated efficiently in the geometric domain because of the one-to-one correspondence between the mixed-adjacency graph and the title representation of the placement. Some pertinent properties of the mixed-adjacency graph and one-dimensional compaction using the graph model are also explored.<>