Abstract:
Distributing large sparse matrix operations in scientific computing is like hypergraph partitioning. Hypergraphs have “hyperedges” that connect any number of nodes. Thus, solving or approximating hypergraph partitioning is NP-hard. Current algorithms solve this problem by iteratively “coarsening” the input hypergraph to smaller problem instances that share key structural features. Interpolating and refining an approximate problem that is small enough to solve directly is possible. However, it is sensitive to coarsening strategy. We use graph embeddings of the initial hypergraph to ensure that coarsened problem instances retrain key structural features. Our method prioritizes coarsening in self-similar regions of the input graph, improving solution quality across a variety of hypergraphs.
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