High-Quality Hypergraph Partitioning

@article{Schlag2020HighQualityHP,
  title={High-Quality Hypergraph Partitioning},
  author={Sebastian Schlag},
  journal={ArXiv},
  year={2020},
  volume={abs/2106.08696}
}
This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer $k$, partition its vertex set into $k$ disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. Since the problem is computationally intractable, heuristics are used in practice - the most prominent… Expand

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References

SHOWING 1-10 OF 544 REFERENCES
Advanced Flow-Based Multilevel Hypergraph Partitioning
TLDR
The recently proposed HyperFlowCutter algorithm for computing bipartitions of unweighted hypergraphs by solving a sequence of incremental maximum flow problems is enhanced to handle weighted instances and a technique for computing maximum flows directly on weighted hyper graphs is proposed. Expand
High Quality Hypergraph Partitioning via Max-Flow-Min-Cut Computations
In this thesis, we introduce a framework based on Max-Flow-Min-Cut computations for improving balanced k-way partitions of hypergraphs. Currently, variations of the FM heuristic [17] are used asExpand
Multilevel Hypergraph Partitioning with Vertex Weights Revisited
TLDR
This work develops an approach based on an assignment of heavy vertices as fixed vertices to both blocks of the bisection (which it is called a prepacking) and uses theoretical results to prove that the balance of the final partition can be guaranteed. Expand
k-way Hypergraph Partitioning via n-Level Recursive Bisection
TLDR
A multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time that forms the basis of the KaHyPar (Karlsruhe Hypergraph Partitioning) framework, which achieves significantly smaller cuts than hMetis and PaToH. Expand
Hypergraph Partitioning and Clustering
  • D. Papa, I. Markov
  • Computer Science
  • Handbook of Approximation Algorithms and Metaheuristics
  • 2007
TLDR
Since partitioning is critical in several practical applications, heuristic algorithms were developed with near-linear runtime, and move-based heuristics for k-way hypergraph partitioning appear in [46, 27, 14]. Expand
Multilevel Algorithms for Multi-Constraint Hypergraph Partitioning
TLDR
New multi-constraint hypergraph partitioning algorithms that are based on the multilevel partitioning paradigm are presented, and a vector of weights is assigned to each vertex, and the goal is to produce a bisection such that the partitioning satisfies a balancing constraint associated with each weight, while attempting to minimize the cut. Expand
n-Level Hypergraph Partitioning
TLDR
A multilevel algorithm for hypergraph partition- ing that contracts the vertices one at a time and thus allows very high quality and has a running time that is comparable to hMetis. Expand
A Multi-level Hypergraph Partitioning Algorithm Using Rough Set Clustering
TLDR
This paper proposes a sequential multi-level hypergraph partitioning algorithm that makes novel use of the technique of rough set clustering in categorising the vertices of the hypergraph. Expand
Evolutionary $n$ -Level Hypergraph Partitioning With Adaptive Coarsening
  • R. Preen, Jim E. Smith
  • Computer Science, Mathematics
  • IEEE Transactions on Evolutionary Computation
  • 2019
TLDR
This paper presents a novel memetic algorithm which remains effective on larger initial hypergraphs and introduces an adaptive scheme that stops coarsening when the rate of information loss in a hypergraph becomes nonlinear and shows that this produces further improvements. Expand
Imbalanced Hypergraph Partitioning and Improvements for Consensus Clustering
TLDR
This work provides a method that finds good approximate solutions under an entropy constraint and further introduces the notion of a discount cut, which helps overcome local optima that frequently plague k-way partitioning algorithms. Expand
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