Hypergraph Clustering via N-Dimensional Placement
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current hypergraph partitioning methods, such as the multi-level partitioning approach using the hMETIS system, are sensitive to initial clustering quality and can get stuck in local minima, with the k-way FM algorithm having linear runtime complexity, making them inefficient for partitioning integrated circuit designs into FPGA units.
Innovation Solution
The method improves clustering by placing the hypergraph into an N-dimensional space, using connectivity-based and hierarchical clustering, and applying the k-harmonic-means algorithm with grid-warping to generate balanced clusters, followed by a single pass of the Fiduccia-Mattheyses algorithm to legalize the partitioning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If multi-level partitioning approach with hMETIS is used, then partitioning can be performed systematically, but the quality of results is sensitive to initial clustering quality and can get stuck in local minima
Solution Approach 1:
The patent transforms the traditional clustering problem by mapping nodes from graph space into N-dimensional Euclidean space. This dimensional transformation allows the use of geometric distance metrics and spatial clustering algorithms (like k-means) that are less prone to getting stuck in local minima compared to traditional graph-based clustering. The N-dimensional placement provides a new perspective for measuring node similarity and forming clusters.
Solution Approach 2:
The patent changes the parameter space by introducing N-dimensional coordinates as new parameters for node representation. Instead of relying solely on graph connectivity metrics, the system uses spatial coordinates (x1, x2, ..., xN) as additional parameters to define node positions. This parameter expansion enables the application of continuous optimization techniques and makes the clustering more robust to initial conditions.
2Reliability
If k-way FM algorithm is used, then partitioning can be performed, but the runtime complexity is linear in k which reduces efficiency
Solution Approach 1:
The patent performs preliminary N-dimensional placement and clustering before applying the FM algorithm. By pre-organizing nodes into clusters based on their N-dimensional positions, the system reduces the search space for the subsequent FM optimization step. This preliminary organization significantly decreases the runtime complexity compared to applying k-way FM directly to the entire graph.
Solution Approach 2:
The patent segments the partitioning process into distinct phases: (1) N-dimensional placement, (2) spatial clustering, and (3) FM optimization. This segmentation allows each phase to focus on specific aspects of the problem, with the spatial clustering phase handling the heavy lifting of initial group formation, thereby reducing the computational burden on the FM algorithm.
3Device complexity
If traditional two-dimensional placement is used for clustering, then simplicity is maintained, but clustering quality is limited
Solution Approach 1:
The patent explicitly moves from traditional two-dimensional placement to N-dimensional placement (where N ≥ 2). This generalization provides more degrees of freedom for node positioning and enables better separation of nodes that would be overlapping or poorly separated in lower dimensions. The increased dimensionality captures more aspects of node relationships, leading to improved clustering quality.
Solution Approach 2:
The patent changes the placement parameters from (x, y) coordinates in 2D space to (x1, x2, ..., xN) coordinates in N-dimensional space. This parameter expansion allows for more nuanced positioning and distance calculations, enabling the clustering algorithm to better distinguish between nodes and form more accurate clusters based on their spatial relationships.
Data Source
AI summary
A method and apparatus to cluster nodes of a hypergraph is described. The method improves the clustering by placing the hypergraph into an N-dimensional space. The method receives a design represented by a hypergraph with a plurality of nodes. The method places the plurality of nodes of the hypergraph into the N-dimensional space, where N is greater than or equal to 2. The method clusters nodes of the hypergraph based on locations of the plurality of nodes in the N-dimensional space.