External memory layout vs. schematic

Abstract

The circuit represented by a VLSI layout must be verified by checking it against the schematic circuit as an important part of the functional verification step. This involves two central problems of matching the circuit graphs with each other (graph isomorphism) and extracting a higher level of circuit from a given level by finding subcircuits in the circuit graph (subgraph isomorphism). Modern day VLSI layouts contain millions of devices. Hence the memory requirements of the data structures required by tools for verifying them become huge and can easily exceed the amount of internal memory available on a computer. In such a scenario, a program not aware of the memory hierarchy performs badly because of its unorganized input/output operations (I/Os) as the speed of a disk access is about a million times slower than accessing a main memory location. In this article, we present I/O-efficient algorithms for the graph isomorphism and subgraph isomorphism problems in the context of verification of VLSI layouts. Experimental results show the need and utility of I/O-efficient algorithms for handling problems with large memory requirements.