SAT based solutions for detailed routing of island style FPGA architectures

Detailed routing solutions for island style FPGA architectures using Boolean satisfiability (SAT) based formulations have been proposed in this paper. Due to decreasing size of ICs and hence, the increasing complexity of the routing resource constraints, routing has been a big challenge in electronic design automation field. Our proposed techniques work on multi-pin net routing where all nets are considered for routing in their intact form whereas, most of the existing routing solutions decompose multi-pin nets into two-pin nets for detailed routing to ease the problem. However this approach, apart from increasing the number of nets in the circuits, may also introduce pin doglegging which, when not permitted by the architecture of FPGA, would require extra constraints to eliminate. Many detailed routers adopt sequential detailed routing approaches which are vulnerable to the net ordering problem which may cause a routable circuit to be erroneously classified as unroutable. Our proposed techniques avoid these pitfalls by keeping the multi-pin nets intact and solve all nets simultaneously using SAT. The SAT-based multi-pin net dogleg-free formulations presented here achieve significant improvement over existing SAT-based solutions with respect to the number of variables and clauses used, thereby achieving greater scalability and also display comparable and sometimes better routability results on benchmark circuits when compared with other detailed routing solutions. Detailed routing is also significantly affected by the architecture of the switching blocks. This paper proposes SAT-based formulation for three different switch box architectures i.e. Subset, Wilton, and Universal switches. Our experiments clearly demonstrate how routing solutions for a circuit can differ significantly for different types of switch boxes.