Safe Hypergraph Contraction via Capacity-Aware Repair Certificates

2026-10-01

AI Summary

This study addresses the challenge in multilevel hypergraph partitioning where vertex contractions satisfying capacity constraints may inadvertently destroy optimal balanced bipartitions. To overcome this, the work proposes a certified safe coarsening approach that introduces pairwise and directed minimum cuts as repair certificates. This mechanism identifies safe contraction operations without requiring prior computation of optimal solutions, and it is rigorously proven to preserve at least one globally optimal feasible partition in hypergraphs with positive integer weights. Integrated into the KaHyPar framework, experimental evaluations on circuit benchmarks demonstrate that the proposed method fully preserves optimality while significantly reducing both best-cut and total cut values, introducing only marginal runtime overhead.

Abstract

Multilevel partitioners shrink circuit hypergraphs through vertex contractions, yet a contraction that satisfies block capacity can still eliminate every optimal balanced bipartition. We develop certified safe coarsening (CSC) to identify contractions that preserve an optimum without computing that optimum. CSC certifies a repair for any feasible partition that splits a candidate group: the repair must respect the fixed block capacities and must not increase the cut-net objective. Its bounds exclude hyperedges that capacity constraints force to be cut. A pair certificate checks individual merges, while a directed minimum-cut test certifies groups whose savings emerge only when vertices move together. We prove that certified disjoint batches and successive rounds with recertification retain at least one globally optimal feasible partition for hypergraphs with positive integer vertex and net weights. Experiments on exactly solvable instances confirm optimum preservation for every tested configuration; integration with KaHyPar lowers the sum of per-instance best cuts on circuit benchmarks, with additional runtime.

Problem

• hypergraph partitioning
• vertex contraction
• multilevel coarsening
• optimal bipartition preservation
• block capacity constraints

Innovation

• Certified Safe Coarsening
• Hypergraph Contraction
• Capacity-Aware Repair
• Multilevel Partitioning
• Directed Minimum-Cut