On a Pin Versus Block Relationship For Partitions of Logic Graphs

Abstract

Partitions of the set of blocks of a computer logic graph, also called a block graph, into subsets called modules demonstrate that a two-region relationship exists between P, the average number of pins per module, and B, the average number of blocks per module. In the first region, P = KBr, where K is the average number of pins per block and 0.57 ≤ r ≤ 0.75. In the second region, that is, where the number of modules is small (i.e., 1-5), P is less than predicted by the above formula and is given by a more complex relationship. These conclusions resulted from controlled partitioning experiments performed using a computer program to partition four logic graphs varying in size from 500 to 13 000 circuits representing three different computers. The size of a block varied from one NOR circuit in one of the block graphs to a 30-circuit chip in one of the other block graphs.