Computing the Representation Polynomial for Directed Acyclic Graphs Using Subgraph Detection and Simplification

The representation polynomial, developed by K. Johnson, is a mathematical equation corresponding to a directed acyclic graph. Johnson’s algorithm is based on decomposing the graph into a set of chain graphs which have a known equation for the representation polynomial. However, the analysis time and computer memory requirements for calculating the representation polynomial for an arbitrary graph of more than ten vertices, from previous implementations [6] of Johnson’s algorithm, is beyond reasonable bounds. Consequently, modifications are made to the implementation of Johnson’s algorithm to decrease the required computation time as well as optimize the allocation of available computer memory. The approach and related results described include antichain graph detection, enhanced chain graph detection, dynamic memory allocation, and graph simplification.