On Aligning Non-Order-Associated Binary Decision Diagrams

Abstract

Recent studies employ collections of binary decision diagrams (BDDs) to solve combinatorial optimization problems. This paper focuses on the problem of optimally aligning two BDDs, that is, transforming them to enforce a common order of variables while keeping the total size of the diagrams as small as possible. We address this problem, which is known to be NP-hard, by introducing and studying a simplified problem instead of working with the more complex original diagrams. We discuss some basic properties of the simplified problem, design a corresponding heuristic for the original problem, and show empirically that this approach yields good quality alignments while significantly reducing the complexity of intermediate diagram transformations. We highlight the practicality of this approach in the context of a variation of the uncapacitated facility location problem. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Funding: This work was supported by the Office of Naval Research [Grant N00014-17-1-2421]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.1293 .