On Aligning Non-Order-Associated Binary Decision Diagrams

Alexey A. Bochkarev, J. Cole Smith

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)910-928
Number of pages19
JournalINFORMS Journal on Computing
Issue number5
StatePublished - Sep 2023


  • analysis of algorithms
  • binary decision diagrams
  • combinatorial optimization problems
  • data structures

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research


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