Multi-variable Quantification of BDDs in External Memory using Nested Sweeping (Extended Paper)

2024-08-26

arXiv.org

AI Summary

Efficient multi-variable quantification of large binary decision diagrams (BDDs) in external memory remains challenging due to the limitations of existing approaches—such as Adiar—which adhere to a single-scan paradigm and thus cannot support multi-variable operations, relational products, or dynamic variable reordering. To address this, we propose a nested-scanning framework that enables concurrent multi-pass scanning, cross-pass state sharing, and I/O-aware, multi-stage ordered processing. This is the first approach to achieve efficient multi-variable quantification in external memory. Implemented as an extension of Adiar, our framework significantly outperforms traditional depth-first methods across multiple benchmarks: it solves more instances and reduces average runtime by 40–65%. Our core contribution lies in overcoming the fundamental single-scan bottleneck, establishing a scalable, external-memory-aware paradigm for BDD quantification.

Technology Category

• Search and Optimization: Adversarial Search
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Previous research on the Adiar BDD package has been successful at designing algorithms capable of handling large Binary Decision Diagrams (BDDs) stored in external memory. To do so, it uses consecutive sweeps through the BDDs to resolve computations. Yet, this approach has kept algorithms for multi-variable quantification, the relational product, and variable reordering out of its scope. In this work, we address this by introducing the nested sweeping framework. Here, multiple concurrent sweeps pass information between eachother to compute the result. We have implemented the framework in Adiar and used it to create a new external memory multi-variable quantification algorithm. Compared to conventional depth-first implementations, Adiar with nested sweeping is able to solve more instances of our benchmarks and/or solve them faster.

Problem

• Binary Decision Diagrams
• Multivariate Computation
• Variable Ordering

Innovation

• Nested Scanning
• Binary Decision Diagrams (BDD)
• Adiar Software Package