K-nearest neighbour (KNN) approach using SAT based technique for rectilinear steiner tree construction

The Rectilinear Steiner Minimum Tree (RSMT) problem claims the minimum length interconnection among a given set of terminals within the rectilinear plane, is one of the basic problems in physical design automation, specifically in routing. Recently, the problem has drawn great attention due to the need for extremely scalable algorithms able to handle nets with large number of terminals. In this paper, a SAT based methodology is introduced for obtaining RSMTs for different nets with varying net degrees. But, the SAT based solutions degrades with the increasing number of Boolean variables. To overcome this scalability issue, a divide-and-conquer approach is proposed here to minimize the solution space. A k-d tree based nearest neighbor (NN) search algorithm is developed here for reducing the solution space and improving the solution quality. Experimental results indicates that the proposed approach are able to obtain a better run time and possess lesser wirelength.