The minimal achievable vertex footprint for hypergraph edge partitioning under independent edge sampling is (1/(2√2)) n / N^{1/d}, with a deterministic partitioner achieving it up to a small constant factor.
Time-efficient and high-quality graph partitioning for graph dynamic scaling,
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Fundamental Limits of Hypergraph Edge Partitioning under Independent Edge Sampling
The minimal achievable vertex footprint for hypergraph edge partitioning under independent edge sampling is (1/(2√2)) n / N^{1/d}, with a deterministic partitioner achieving it up to a small constant factor.