SpecPart

Abstract

State-of-the-art hypergraph partitioners follow the multilevel paradigm that constructs multiple levels of progressively coarser hypergraphs that are used to drive cutsize refinement on each level of the hierarchy. Multilevel partitioners are subject to two limitations: (i) hypergraph coarsening processes rely on local neighborhood structure without fully considering the global structure of the hypergraph; and (ii) refinement heuristics risk entrapment in local minima. In this paper, we describe K-SpecPart, the first supervised spectral framework that directly tackles these two limitations. K-SpecPart solves a generalized eigenvalue problem that captures the balanced partitioning objective and global hypergraph structure in a low-dimensional vertex embedding while leveraging initial high-quality solutions from multilevel partitioners as hints. Specifically, in the context of multi-way partitioning, K-SpecPart derives multiple bipartitioning solutions from a multi-way hint partitioning solution. These bipartitioning solutions are independently integrated into the generalized eigenvalue problem to compute several eigenvectors, inducing a large-dimensional embedding. We apply Linear Discriminant Analysis (LDA) to transform this large-dimensional embedding into a lower-dimensional embedding. K-SpecPart further constructs a family of trees from the vertex embedding and partitions them with a tree-sweeping algorithm. We extend the tree partitioning algorithm of SpecPart [30] to handle multiway partitioning. The multiple tree-based partitioning solutions are overlaid, followed by lifting to a clustered hypergraph, where an ILP (integer linear programming) partitioning problem instance is solved. Our empirical studies substantiate the benefits of K-SpecPart. For bipartitioning, K-SpecPart produces superior solutions to SpecPart with improvements in some cases of up to ∼30%. For multi-way partitioning, K-SpecPart produces superior solutions to hMETIS and KaHyPar with improvements in some cases of up to ∼20%.

The TILOS AI Institute: Integrating optimization and AI for chip design, networks, and robotics

“…At the same time, progress of optimization methods requires a clearly illuminated leading edge, as even very well-studied optimizations may be far from well-solved. (For example, the state of the art for the classic hypergraph mincut partitioning optimization remained static for a quarter-century, until results last year in Bustany et al (2022)). The resulting challenge for both research and culture change is to develop new principles and mechanisms that provide a foundation for fair benchmarking.…”

“…(For example, the state of the art for the classic hypergraph min‐cut partitioning optimization remained static for a quarter‐century, until results last year in Bustany et al. (2022)). The resulting challenge for both research and culture change is to develop new principles and mechanisms that provide a foundation for fair benchmarking.…”