An efficient algorithm for generation of loop-tree basis in 2.5D interconnect models

An efficient algorithm for obtaining the loop-tree decomposition of the method of moment (MoM) basis is proposed. The set of loops consists of two parts - the small loops formed around the vertices of the MoM mesh and the superloops generated as a result of sequential addition of via connections to the interconnect model. The process of forming the superloops involves N^V-steps, N^Vbeing the number of vias in the interconnect model. The method is based on repetitive execution of well-known tree generation algorithm and the shortest path search algorithm. Both of these algorithms scale as O(N), where N is the size of MoM mesh, resulting in O(N^V N) total complexity of the proposed loop generation process.