k-way Hypergraph Partitioning via n-Level Recursive Bisection

Schlag, Sebastian; Henne, Vitali; Heuer, Tobias; Meyerhenke, Henning; Sanders, Peter; Schulz, Christof

doi:10.48550/arxiv.1511.03137

Cited by 2 publications

(4 citation statements)

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“…This is achieved by carefully parallelizing and engineering each phase of the multilevel framework. To further improve solution quality, future work includes parallelizing flow-based refinement techniques [20,22,26] as well as KaHyPar's n-level hierarchy approach [3,52]. Additionally, we want to speed up our FM implementation, and improve the solution quality of label propagation, e.g., using hill-scanning [36] or caching negative gain moves to enable otherwise infeasible high-gain moves.…”

Section: Discussionmentioning

confidence: 99%

“…We compute initial k-way partitions via multilevel recursive bipartitioning using our parallel coarsening and refinement. Initial 2-way partitions on the coarsest hypergraphs are computed with the same portfolio of algorithms that is used in KaHyPar [52]. The portfolio contains 9 different sequential algorithms, including greedy hypergraph growing [12], random assignment, hypergraph growing with label propagation, and alternating BFS [25].…”

Section: Initial Partitioningmentioning

confidence: 99%

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Scalable Shared-Memory Hypergraph Partitioning

Gottesbüren

Heuer

Sanders

et al. 2021

2021 Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX)

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We present a shared-memory algorithm to compute high-quality solutions to the balanced k-way hypergraph partitioning problem. This problem asks for a partition of the vertex set into k disjoint blocks of bounded size that minimizes the connectivity metric (i.e., the sum of the number of different blocks connected by each hyperedge). High solution quality is achieved by parallelizing the core technique of the currently best sequential partitioner KaHyPar: the most extreme n-level version of the widely used multilevel paradigm, where only a single vertex is contracted on each level. This approach is made fast and scalable through intrusive algorithms and data structures that allow precise control of parallelism through atomic operations and fine-grained locking. We perform extensive experiments on more than 500 real-world hypergraphs with up to 140 million vertices and two billion pins (sum of hyperedge sizes). We find that our algorithm computes solutions that are on par with a comparable configuration of KaHyPar while being an order of magnitude faster on average. Moreover, we show that recent non-multilevel algorithms specifically designed to partition large instances have considerable quality penalties and no clear advantage in running time.

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Section: Discussionmentioning

confidence: 99%

Section: Initial Partitioningmentioning

confidence: 99%

Scalable Shared-Memory Hypergraph Partitioning

Gottesbüren

Heuer

Sanders

et al. 2021

2021 Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX)

Self Cite

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show abstract

“…This process is repeated until the algorithm can no longer find any non-singleton clusters or the number of hypernodes drops below 160k. The second condition is the same stopping criteria used in [62].…”

Section: Acyclic Coarseningmentioning

confidence: 99%

“…k-way FM Refinement. The k-way FM refinement aims to improve a given k-way partition and is based on the k-way FM refinement algorithm implemented in KaHyPar [62]. The algorithm maintains k PQs, one queue for each block.…”

Section: Acyclic Refinementmentioning

confidence: 99%

Multilevel Acyclic Hypergraph Partitioning

Popp¹,

Schlag²,

Schulz³

et al. 2020

Preprint

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A directed acyclic hypergraph is a generalized concept of a directed acyclic graph, where each hyperedge can contain an arbitrary number of tails and heads. Directed hypergraphs can be used to model data flow and execution dependencies in streaming applications. Thus, hypergraph partitioning algorithms can be used to obtain efficient parallelizations for multiprocessor architectures. However, an acyclicity constraint on the partition is necessary when mapping streaming applications to embedded multiprocessors due to resource restrictions on this type of hardware. The acyclic hypergraph partitioning problem is to partition the hypernodes of a directed acyclic hypergraph into a given number of blocks of roughly equal size such that the corresponding quotient graph is acyclic while minimizing an objective function on the partition.Here, we contribute the first n-level algorithm for the acyclic hypergraph partitioning problem. Our focus is on acyclic hypergraphs where hyperedges can have one head and arbitrary many tails. Based on this, we engineer a memetic algorithm to further reduce communication cost, as well as to improve scheduling makespan on embedded multiprocessor architectures. Experiments indicate that our algorithm outperforms previous algorithms that focus on the directed acyclic graph case which have previously been employed in the application domain. Moreover, our experiments indicate that using the directed hypergraph model for this type of application yields a significantly smaller makespan. PRACTICAL MOTIVATIONThis research is inspired by computer vision and imaging applications which typically have a high demand for computational power. Quite often, these applications run on embedded devices that have limited compute resources and also a tight thermal budget. This requires the use of specialized hardware and a programming model that allows to fully utilize the compute resources for streaming applications. Directed hypergraphs can be used to model data flow and execution dependencies in streaming applications. Thus, hypergraph partitioning algorithms can be used to obtain efficient parallelizations for multiprocessor architectures. However, when mapping streaming applications to embedded multiprocessors, memory-size restrictions on this type of hardware require the partitioning to be acyclic. The problem is NP-complete [47], and Partially supported by DFG grants DFG SA 933/11-1 and SCHU 2567/1-2.

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k-way Hypergraph Partitioning via n-Level Recursive Bisection

Cited by 2 publications

References 0 publications

Scalable Shared-Memory Hypergraph Partitioning

Scalable Shared-Memory Hypergraph Partitioning

Multilevel Acyclic Hypergraph Partitioning

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