Engineering a direct <i>k</i>-way Hypergraph Partitioning Algorithm

Akhremtsev, Yaroslav; Heuer, Tobias; Sanders, Peter; Schlag, Sebastian

doi:10.1137/1.9781611974768.3

Cited by 48 publications

(89 citation statements)

References 55 publications

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“…The algorithm we propose in Section III encodes all possible choices of distribution in a hypergraph, and so our optimisation procedure relies solely on a hypergraph partitioner. The latter programs have been extensively studied and perfected in the computer science literature to perform efficiently even for large inputs [24,25]. Unlike the former work [36], our approach may distribute circuits across any number of QPUs, thus answering an open problem proposed by the previous authors.…”

Section: The Circuit Distribution Problemmentioning

confidence: 99%

“…Reducing the problem to hypergraph partitioning lets us use third-party solvers such as KaHyPar [24]. We implemented this approach in the quantum circuit description language Quipper [39]; the code is available at [40].…”

Section: B Implementationmentioning

confidence: 99%

“…This document develops an automated method that distributes any circuit across any number of quantum processing units, while minimising the quantum communication between them. We reduce the problem to hypergraph partitioning, which has been extensively researched in computer science literature and has fast heuristic solvers [24,25]. We first discuss distributed quantum computing in more detail, then we reduce the problem of distributing a circuit across multiple QPUs to hypergraph partitioning.…”

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confidence: 99%

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Automated distribution of quantum circuits via hypergraph partitioning

Andrés-Martínez

Heunen

2019

Phys. Rev. A

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Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits over multiple agents, minimising quantum communication between them. We reduce the problem to hypergraph partitioning and then solve it with state-of-the-art optimisers. This makes our approach useful in practice, unlike previous methods. Our implementation is evaluated on five quantum circuits of practical relevance.PACS numbers: 03.67.Ac; 03.67.Lx I. INTRODUCTIONQuantum computation [1-3] employs the laws of quantum mechanics to design systems capable of outperforming classical computers in certain problems [4][5][6]. Over the past couple of decades, this idea has rapidly developed from theoretical results into actual quantum technology [7][8][9].Although there are other approaches [10], the dominant way to present a quantum algorithm is as a quantum circuit [11]: a description of how quantum devices, chosen from a fixed finite set, are applied to different parts of the input system; see Figure 1 for an example. Each of the 'wires' that quantum devices act upon typically consist of a two level quantum system called a quantum bit or qubit. The qubit count grows with the input size, and for relevant problems such as the unique shortest vector problem (with applications in cryptography [12]) the circuit grows large: lattice dimension 3 already requires 842 qubits and 95,624 gates [13].Near-term quantum computing architectures are not capable of executing such large circuits. We are currently entering the era of Noisy Intermediate-Scale Quantum (NISQ) technology [14], being able to fabricate small quantum computing units (QPU for short) ranging from 10 to almost 100 qubits. Much effort is being dedicated to further increase the number of qubits that QPUs can manage, but as the number of qubits grows, the challenge of addressing each qubit individually and shielding them from unwanted interactions and decoherence rapidly becomes unmanageable [15]. To scale up beyond this point, researchers are proposing distributed quan-

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Section: The Circuit Distribution Problemmentioning

confidence: 99%

Section: B Implementationmentioning

confidence: 99%

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confidence: 99%

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Automated distribution of quantum circuits via hypergraph partitioning

Andrés-Martínez

Heunen

2019

Phys. Rev. A

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“…The triangulation of the sample point set is computed sequentially using CGAL [19] with exact predicates. 2 The closest sample point for a given input point in Line 8 of Algorithm 2 can be found via the Voronoi diagram of the sample triangulation. However, using the lightweight k-D tree implementation nanoflann 3 proved to be more efficient.…”

Section: Implementation Notesmentioning

confidence: 99%

Load-Balancing for Parallel Delaunay Triangulations

Funke

Sanders

Winkler

2019

Lecture Notes in Computer Science

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Computing the Delaunay triangulation (DT) of a given point set in R D is one of the fundamental operations in computational geometry. Recently, Funke and Sanders [18] presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices -the border vertices -and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.Recently, we presented a novel divide-and-conquer (D&C) DT algorithm for arbitrary dimension [18] that lends itself equally well to shared and distributed memory parallelism and thus hybrid parallelization. While previous D&C DT algorithms suffer from a complex -often sequential -divide or merge step [12,24], our algorithm reduces the merging of two partial triangulations to re-triangulating a small subset of their vertices -the border vertices -using the same parallel algorithm and combining the three triangulations efficiently via hash table lookups. All steps required for the merging -identification of relevant vertices, triangulation and combining the partial DTs -are performed in parallel.The division of the input points in the divide-step needs to address a twofold sensitivity to the point distribution: the partitions need to be approximately equal-sized for good load-balancing, arXiv:1902.07554v1 [cs.DS]

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“…Project (P7) has significantly contributed to the large body of previous work in the area; see [10] for an overview. Their recent k-way partitioning result [1] represents the state of art concerning highquality hypergraph partitioning: it always computes better solutions and is faster than some of the competitors.…”

Section: P7 Engineering Algorithms For Partitioning Large Graphsmentioning

confidence: 99%

DFG Priority Programme SPP 1736: Algorithms for Big Data

Behdju

Meyer

2017

Künstl Intell

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Volume, Velocity, and Variety are the three Vs commonly used to define the term big data. Simply put, those refer to the increasing amount of new data created, the increasing rate at which it is created, and the increasing number of different formats it has. At the same time, the three Vs describe challenges that require new algorithmic approaches. In order to tackle those challenges, the German Research Foundation established in 2013 the priority programme SPP 1736: Algorithms for Big Data. In this article we give a short overview on the research topics represented within this priority programme.

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Engineering a direct k-way Hypergraph Partitioning Algorithm

Cited by 48 publications

References 55 publications

Automated distribution of quantum circuits via hypergraph partitioning

Automated distribution of quantum circuits via hypergraph partitioning

Load-Balancing for Parallel Delaunay Triangulations

DFG Priority Programme SPP 1736: Algorithms for Big Data

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