Hypergraph Partitioning via Correlation Meta-Heuristic Seed Generation
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Solution Overview
Problem
The quality of results in hypergraph partitioning, particularly in electronic design automation for integrated circuit design, is sensitive to the initial solution and prone to getting stuck in local minima, which affects the efficiency of partitioning into FPGA units, especially when considering timing and wire configuration constraints.
Innovation Solution
A correlation meta-heuristic system that tracks node assignments and correlations between pairs of nodes to generate improved seed solutions for local search, using an assignment and correlation history to guide the search process and update information after each trial, thereby improving the partitioning results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If multiple trials of local search are run with different seed solutions, then the quality of partitioning results is improved, but the computational time and complexity increase
Solution Approach 1:
The patent applies preliminary action by performing a coarsening phase before local search, where the hypergraph is simplified and partitioned at a higher level. This preliminary partitioning provides better initial seed solutions for the subsequent local search trials, improving the quality of final partitioning results while reducing the need for excessive trials and thus limiting computational time expenditure.
Solution Approach 2:
The patent implements feedback by using the results from coarsening and previous partitioning trials to inform and improve subsequent trials. The uncoarsening phase feeds back refined partitioning information to guide further local search, creating an iterative improvement process that achieves high-quality results more efficiently than random multiple trials alone.
2Manufacturing precision
If local search optimization is applied repeatedly, then partitioning quality improves, but the algorithm gets stuck in local minima
Solution Approach 1:
The patent applies segmentation by dividing the partitioning process into distinct phases: coarsening, local search, and uncoarsening. Each phase operates at a different level of detail and serves a specific purpose. The coarsening phase handles high-level structure, local search refines within that structure, and uncoarsening integrates results. This segmentation prevents the algorithm from getting stuck in local minima by changing the search landscape between phases.
Solution Approach 2:
The patent implements dynamics by transitioning between different levels of hypergraph abstraction (coarse and fine) and adjusting the search strategy accordingly. The algorithm dynamically switches between exploration (coarsening with broader search) and exploitation (local search with focused refinement), preventing premature convergence to suboptimal solutions while maintaining reliability.
3Productivity
If coarsening is used to reduce problem size, then computational efficiency improves, but the initial solution quality becomes sensitive and affects final results
Solution Approach 1:
The patent applies preliminary action by carefully designing the coarsening phase to create a simplified hypergraph structure that preserves essential partitioning characteristics. This preliminary structuring ensures that even though the problem size is reduced for computational efficiency, the initial solution quality remains high because the coarsening process maintains critical connectivity and partitioning information.
Solution Approach 2:
The patent uses dimensionality change by transitioning between different levels of abstraction (from fine-grained to coarse-grained hypergraph representation). This dimensional transformation allows efficient computation at the coarse level while the uncoarsening phase reconstructs the fine-grained solution, maintaining both computational efficiency and solution quality through multi-scale analysis.
Data Source
AI summary
A method for partitioning for a hypergraph including a plurality of nodes into a plurality of bins includes assigning each node of the hypergraph to one of the plurality of bins to generate a candidate solution, and for each pair of nodes in the candidate solution, calculating a weighted covariance based on the bin assignment of each node of the pairs of nodes in the candidate solution. The assigning and the calculating are repeated to generate an accumulated weighted covariance for the pairs of nodes, from which a seed partition of the hypergraph is generated.