Multi terminal net routing for island style FPGAs using nearly-2-SAT computation

Detailed routing for multi terminal nets have been proposed in this paper for island style FPGA architectures. The demand of integrated circuits and their decreasing size keep the research on physical design automation alive. In the proposed technique, the detailed routing constraints for island style FPGAs are created in such a way that they can be represented as a set of Conjunctive Normal Form (CNF) clauses. The routing problem is implicitly conceptualized as a graph node colouring problem which is then expressed as a satisfiability problem where most of the clauses consist of 2 literals. Hence, the routing problem is represented as a “nearly-2-SAT” problem. 2-SAT, i.e. satisfiability of a CNF function with clauses of at most 2 literals, is polynomial time computable, whereas 3-SAT or more are NP-complete. The “nearly-2-SAT” conversion of the routing problem proposed here requires less number of clauses to formulate the routing function w.r.t the existing SAT-based routing techniques. In addition, more than 95% of clauses are of 2-literal which increases the efficiency and scalability of the technique.