Selection of efficient re-ordering heuristics for MDD construction

Abstract

Multi-valued decision diagrams (MDDs) are a generalization of binary decision diagrams (BDDs). They are suitable for several applications in synthesis and verification of integrated circuits since often, functions with multi-valued input variables can be represented efficiently by MDDs. Their sizes counted in number of nodes vary from linear to exponential dependent on the variable ordering used. Therefore sifting, i.e. dynamic variable re-ordering, has to be applied frequently while an MDD is built in order to keep the number of nodes needed during the process small. Often most of the runtime for MDD construction is spent for sifting. We present a new method that speeds up MDD construction and also reduces memory consumption. It is based on the selection of re-ordering heuristics dependent on the history of the construction process. Success of previous re-ordering steps as well as the frequency of sifting calls in the past are used to determine a variation of sifting that is applied next. Experimental results are given to demonstrate that runtimes and memory consumption can be reduced by 30% on average when the proposed selection methods are used during MDD construction.