e-boost: Boosted E-Graph Extraction with Adaptive Heuristics and Exact Solving

2025-08-18

AI Summary

E-graph extraction is an NP-hard combinatorial optimization problem and constitutes the primary performance bottleneck in e-graph optimization. Conventional approaches struggle to balance solution speed and quality: heuristic methods are efficient but suboptimal, while exact methods guarantee optimality at prohibitive computational cost. This paper proposes a novel framework integrating parallel heuristic search, adaptive pruning, and warm-start exact solving. Specifically, it employs parallel DAG cost evaluation, parameterized threshold-based pruning, and ILP-based initialization for exact solving—jointly enhancing both efficiency and optimality. On multiple benchmarks, our method achieves a 558× speedup over standard ILP solvers and delivers an average 19.04% performance improvement over the state-of-the-art SmoothE framework. In real-world synthesis tasks, it yields 7.6%–8.1% area reduction.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Search
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

E-graphs have attracted growing interest in many fields, particularly in logic synthesis and formal verification. E-graph extraction is a challenging NP-hard combinatorial optimization problem. It requires identifying optimal terms from exponentially many equivalent expressions, serving as the primary performance bottleneck in e-graph based optimization tasks. However, traditional extraction methods face a critical trade-off: heuristic approaches offer speed but sacrifice optimality, while exact methods provide optimal solutions but face prohibitive computational costs on practical problems. We present e-boost, a novel framework that bridges this gap through three key innovations: (1) parallelized heuristic extraction that leverages weak data dependence to compute DAG costs concurrently, enabling efficient multi-threaded performance without sacrificing extraction quality; (2) adaptive search space pruning that employs a parameterized threshold mechanism to retain only promising candidates, dramatically reducing the solution space while preserving near-optimal solutions; and (3) initialized exact solving that formulates the reduced problem as an Integer Linear Program with warm-start capabilities, guiding solvers toward high-quality solutions faster. Across the diverse benchmarks in formal verification and logic synthesis fields, e-boost demonstrates 558x runtime speedup over traditional exact approaches (ILP) and 19.04% performance improvement over the state-of-the-art extraction framework (SmoothE). In realistic logic synthesis tasks, e-boost produces 7.6% and 8.1% area improvements compared to conventional synthesis tools with two different technology mapping libraries. e-boost is available at https://github.com/Yu-Maryland/e-boost.

Problem

• E-graph extraction is NP-hard and performance-critical
• Heuristic methods lack optimality, exact methods are too slow
• Need efficient near-optimal extraction for logic synthesis/verification

Innovation

• Parallelized heuristic extraction for multi-threaded performance
• Adaptive search space pruning with threshold mechanism
• Initialized exact solving using Integer Linear Program