An Optimal Alignment-Driven Iterative Closed-Loop Convergence Framework for High-Performance Ultra-Large Scale Layout Pattern Clustering

TL;DR

This work tackles the NP-hard problem of ultra-large-scale layout pattern clustering in DFM by introducing an Optimal Alignment-Driven Iterative Closed-Loop Framework. It combines two high-performance alignment engines (FFT-based Phase Correlation and a Geometric Min-Max approach) with a coarse-to-fine iterative workflow and a Surprisal-Based Lazy Greedy SCP solver to achieve rapid convergence and high-quality clustering. The framework employs aggressive pre-screening, multi-stage pruning, and parallel optimizations to deliver over 100× speedups and 93.4% compression on large benchmarks, securing top ranking in a major challenge. The approach offers a scalable, precise solution for OPC and related DFM tasks on ultra-large pattern sets, with strong practical impact for industrial EDA workflows.

Abstract

With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with computational prohibitiveness ($O(N^2)$ comparisons), sub-optimal discrete sampling for center alignment, and difficult speed-quality trade-offs. To address these, we propose an Optimal Alignment-Driven Iterative Closed-Loop Convergence Framework. First, to resolve alignment ambiguity, we introduce a hybrid suite of high-performance algorithms: an FFT-based Phase Correlation method for cosine similarity constraints, and a Robust Geometric Min-Max strategy for edge displacement constraints that analytically solves for the global optimum. Second, we model clustering as a Set Cover Problem (SCP) using a Surprisal-Based Lazy Greedy heuristic within a coarse-to-fine iterative refinement loop to ensure convergence. Additionally, a multi-stage pruning mechanism filters over 99% of redundant computations. Experimental results on the 2025 China Postgraduate EDA Elite Challenge benchmark demonstrate a 93.4% compression ratio relative to raw inputs and an over 100x speedup compared to the official baseline, effectively handling tens of thousands of patterns in seconds. Securing First Place among 77 teams, this approach proves its superiority in solving the NP-Hard layout clustering problem with an optimal balance of scalability and precision.

Figures (7)

• Figure 1: Overview of the critical role of pattern clustering in accelerating VLSI DFM flow.
• Figure 2: Challenges and limitations of existing layout clustering methods.
• Figure 3: Overview of the clustering workflow and similarity constraints.
• Figure 4: Architecture of the proposed Optimal Alignment-Driven Iterative Closed-Loop Framework.
• Figure 5: Illustration of the optimal alignment process and similarity maximization. Unlike centroid-based alignment, optimal alignment actively searches for the translation vector $T_{opt}$ that maximizes the overlap between patterns.