On the Minimization of Average Path Lengths for Heterogeneous MDDs

In this paper, we propose an exact and a heuristic minimization algorithms for the average path length (APL) of heterogeneous multi-valued decision diagrams (MDDs). In a heterogeneous MDD, each variable can take on the different number of values. To represent a binary logic function using a heterogeneous MDD, we partition the binary variables into groups, and treat them as multi-valued variables. By considering partitions of binary variables, we can obtain heterogeneous MDDs that represent logic functions more compactly and have smaller APLs than reduced ordered binary decision diagrams (ROBDDs). Experimental results using 21 benchmark functions show that the APLs of the heterogeneous MDDs can be reduced by a half that of corresponding ROBDDs, on average, without increasing memory size