An Efficient Subcircuit Recognition Using the Nonlinear Graph Matching

Subcircuit recognition (SR) is a problem of identifying all instances of a small subcircuit in a larger circuit. Despite recent progress toward the linear graph matching based SR algorithms, finding a large set of subcircuits in a multi-million circuit may be still prohibitively long for many IC CAD applications. In this paper we develop a new efficient SR method using a nonlinear graph matching strategy. Namely, our method employs an advanced nonlinear technique to minimize the objective function (OF) associated with the SR problem. Unlike the linear graph matching we don´t approximate the OF by the first-order terms in its Taylor series expansion. In contrast, the second-order terms are exploited to form a set of nonlinear equations (SNE) that describe the net and device match probabilities. To solve the obtained SNE we use a nonlinear version of the Kaczmarz method (KM). We improve the KM efficiency by making two modifications in its updating scheme; this leads to fast and stable convergence of the SR process. The experimental results show that the new method is on average three times faster compared to the linear graph matching algorithms