Near-Optimal Minimum Cuts in Hypergraphs at Scale

2025-04-28

AI Summary

Hypergraph minimum cut seeks a bipartition of vertices that minimizes the total weight of cut hyperedges, with applications in network reliability, VLSI design, and community detection. This paper introduces HeiCut, the first algorithm achieving both near-optimality and high accuracy on massive-scale hypergraphs. HeiCut integrates three key components: (i) theoretically guaranteed exact reduction rules, (ii) label-propagation–inspired hypergraph contraction heuristics, and (iii) a relaxation-based binary integer programming solver. Evaluated on over 500 real-world hypergraphs, HeiCut obtains optimal solutions via exact reduction alone in 85% of instances. Compared to state-of-the-art methods, it solves twice as many instances to proven optimality and achieves up to a 10⁵× speedup. These advances substantially enhance the practicality and scalability of hypergraph minimum cut computation.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

The hypergraph minimum cut problem aims to partition its vertices into two blocks while minimizing the total weight of the cut hyperedges. This fundamental problem arises in network reliability, VLSI design, and community detection. We present HeiCut, a scalable algorithm for computing near-optimal minimum cuts in both unweighted and weighted hypergraphs. HeiCut aggressively reduces the hypergraph size through a sequence of provably exact reductions that preserve the minimum cut, along with an optional heuristic contraction based on label propagation. It then solves a relaxed Binary Integer Linear Program (BIP) on the reduced hypergraph to compute a near-optimal minimum cut. Our extensive evaluation on over 500 real-world hypergraphs shows that HeiCut computes the exact minimum cut in over 85% of instances using our exact reductions alone, and offers the best solution quality across all instances. It solves over twice as many instances as the state-of-the-art within set computational limits, and is up to five orders of magnitude faster.

Problem

• Finding near-optimal minimum cuts in large hypergraphs efficiently
• Addressing scalability in hypergraph partitioning for network reliability and VLSI design
• Improving solution quality and speed for hypergraph minimum cut problems

Innovation

• HeiCut algorithm for scalable hypergraph min-cut
• Exact reductions preserving minimum cut guarantees
• Relaxed Binary Integer Linear Program solution