  Hypergraphs allow modeling problems with multi-way high-order relationships.
However, the computational cost of most existing hypergraph-based algorithms
can be heavily dependent upon the input hypergraph sizes. To address the
ever-increasing computational challenges, graph coarsening can be potentially
applied for preprocessing a given hypergraph by aggressively aggregating its
vertices (nodes). However, state-of-the-art hypergraph partitioning
(clustering) methods that incorporate heuristic graph coarsening techniques are
not optimized for preserving the structural (global) properties of hypergraphs.
In this work, we propose an efficient spectral hypergraph coarsening scheme
(HyperSF) for well preserving the original spectral (structural) properties of
hypergraphs. Our approach leverages a recent strongly-local max-flow-based
clustering algorithm for detecting the sets of hypergraph vertices that
minimize ratio cut. To further improve the algorithm efficiency, we propose a
divide-and-conquer scheme by leveraging spectral clustering of the bipartite
graphs corresponding to the original hypergraphs. Our experimental results for
a variety of hypergraphs extracted from real-world VLSI design benchmarks show
that the proposed hypergraph coarsening algorithm can significantly improve the
multi-way conductance of hypergraph clustering as well as runtime efficiency
when compared with existing state-of-the-art algorithms.
