Defect-aware nanocrossbar logic mapping using Bipartite Subgraph Isomorphism & canonization

This paper addresses the NP-complete problem of mapping a logic function on to a nanocrossbar with a known defect map. We first show that this problem can be transformed into a Bipartite SubGraph Isomorphism (BSGI) problem. Then we present our proposed KNS-2DS algorithm, which canonizes both graphs in N² time (N being the number of nodes) and then matches them in N³ time in the worst case. KNS-2DS uses a K-Neighbor Sort (KNS) to initialize our main contribution 2D-Sort (2DS). 2DS is an iterative rough canonizer that lets a straightforward matching algorithm complete the job. Our algorithm offers very short run-times (due to canonization) compared to previous work and has success on all benchmarks. KNS-2DS is also novel from the perspective of the BSGI problem in the sense that it is based on canonization but not on a search tree with backtracking.