Adiar Binary Decision Diagrams in External Memory

Abstract

We follow up on the idea of Lars Arge to rephrase the Reduce and Apply operations of Binary Decision Diagrams (BDDs) as iterative I/O-efficient algorithms. We identify multiple avenues to simplify and improve the performance of his proposed algorithms. Furthermore, we extend the technique to other common BDD operations, many of which are not derivable using Apply operations alone. We provide asymptotic improvements to the few procedures that can be derived using Apply.Our work has culminated in a BDD package named Adiar that is able to efficiently manipulate BDDs that outgrow main memory. This makes Adiar surpass the limits of conventional BDD packages that use recursive depth-first algorithms. It is able to do so while still achieving a satisfactory performance compared to other BDD packages: Adiar, in parts using the disk, is on instances larger than 9.5 GiB only 1.47 to 3.69 times slower compared to CUDD and Sylvan, exclusively using main memory. Yet, Adiar is able to obtain this performance at a fraction of the main memory needed by conventional BDD packages to function.

HermesBDD: A Multi-Core and Multi-Platform Binary Decision Diagram Package

“…Based on the work of Lars Arge [11], Adiar [12] is a singlecore BDD package that makes use of time-forward processing to improve the I/O complexity of BDD manipulation. This achieves efficient manipulation of BDDs, even when they outgrow the memory limit of a given machine.…”