# Partitioning Hypergraphs is Hard: Models, Inapproximability, and Applications

arXiv: https://arxiv.org/abs/2208.08257 · HTML: https://mlsanity.com/paper/2208.08257/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2022.

## Built on by (most cited first, 1 of 1)

- [Practical Performance Guarantees for Pipelined DNN Inference](https://mlsanity.com/paper/2311.03703/) (2023)

## Abstract (arXiv)

We study the balanced k-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on n nodes, our goal is to partition the node set into k parts of size at most (1+ε)· fracnk each, while minimizing the cost of the partitioning, defined as the number of cut hyperedges, possibly also weighted by the number of partitions they intersect. We show that this problem cannot be approximated to within a n1/poly loglog n factor of the optimal solution in polynomial time if the Exponential Time Hypothesis holds, even for hypergraphs of maximal degree 2. We also study the hardness of the partitioning problem from a parameterized complexity perspective, and in the more general case when we have multiple balance constraints. Furthermore, we consider two extensions of the partitioning problem that are motivated from practical considerations. Firstly, we introduce the concept of hyperDAGs to model precedence-constrained computations as hypergraphs, and we analyze the adaptation of the balanced partitioning problem to this case. Secondly, we study the hierarchical partitioning problem to model hierarchical NUMA (non-uniform memory access) effects in modern computer architectures, and we show that ignoring this hierarchical aspect of the communication cost can yield significantly weaker solutions.