Minimization of average path length in BDDs by variable reordering

Abstract : Minimizing the Average Path Length (APL) in a BDD reduces the time needed to evaluate Boolean functions represented by BDDs. This paper describes an efficient heuristic APL minimization procedure based on BDD variable reordering. The reordering algorithm is similar to classical variable sifting with the cost function equal to the APL rather than the number of BDD nodes. The main contribution of our paper is a fast way of updating the APL during the swap of two adjacent variables. Experimental results show that the proposed algorithm effectively minimizes the APL of large MCNC benchmark functions, achieving reductions of up to 47%. For some benchmarks, minimizing APL also reduces the BDD node count.

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