An implicit connection graph maze routing algorithm for ECO routing

ECO routing is a very important design capability in advanced IC, MCM and PCB designs when additional routings need to be made at the latter stage of the physical design. ECO is difficult in two aspects: first, there are a large number of existing interconnects which become obstacles in the region. A hierarchical approach is not applicable in this situation, and we need to search a large, congested region thoroughly. Second, advances in circuit designs require variable width and variable spacing on interconnects. Thus, a gridless routing algorithm is needed. We propose to use an implicit representation of a non-uniform grid graph for a gridless maze routing algorithm. A novel slit-tree plus interval-tree data structure is developed, combined with a cache structure, to support efficient queries into the connection graph. Our experiments show that this data structure is very small in memory usage while very fast in answering maze expansion related queries. This makes the framework very useful in the ECO type of routing.