Abstract:Multi-constraint hypergraph partitioning is a generalization of balanced partitioning, where the vertex set of a hypergraph is partitioned such that the inter-block connectivity of hyperedges is minimized while balancing the vertices with regard to $d$ distinct constraints. A prominent class of applications is data distribution tasks, where this allows to achieve good load balance for $d$ different kinds of resources and simultaneously minimize the communication volume.
Although the best approaches for single-constraint partitioning are usually complex (multilevel) algorithms with many components, we show that replacing only one component already leads to high-quality multi-constraint partitions: the rebalancing step, which restores balance for a partition that has (hopefully) small connectivity but violates the constraints. We design a multi-constraint rebalancing algorithm based on greedy local search, proving that balance is always restored for $d=2$ and bounded maximum weight. The key is to ensure monotonically decreasing global imbalance by choosing an imbalance metric where there is always a balance-improving move available. Integrating our algorithm into the state-of-the-art partitioner Mt-KaHyPar, we demonstrate an 11.5% geometric mean connectivity reduction compared to the next best competitor (Metis) and better reliability regarding partition balance, even though the majority of inputs is outside of the theoretical guarantee.
From: Nikolai Maas [view email]
[v1]
Wed, 27 May 2026 11:36:57 UTC (1,399 KB)
[v2]
Wed, 15 Jul 2026 12:51:42 UTC (2,097 KB)
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