Write-Avoiding Algorithms

Carson, Erin; Demmel, James; Grigori, Laura; Knight, Nicholas; Koanantakool, Penporn; Schwartz, Oded; Simhadri, Harsha Vardhan

doi:10.1109/ipdps.2016.114

Cited by 25 publications

(16 citation statements)

References 26 publications

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“…(Likewise, time complexity is usually measured with respect to the number of words in the input, with the assumption that arithmetic operations on words can be performed in constant time.) The practical relevance of studying problems in the constant workspace model is increasing, as there are many current and emerging memory technologies where writing can be much more expensive than reading in terms of time and energy [Carson et al 2016].…”

Section: Introductionmentioning

confidence: 99%

Common Tangents of Two Disjoint Polygons in Linear Time and Constant Workspace

Abrahamsen

Walczak

2018

ACM Trans. Algorithms

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We provide a remarkably simple algorithm to compute all (at most four) common tangents of two disjoint simple polygons. Given each polygon as a read-only array of its corners in cyclic order, the algorithm runs in linear time and constant workspace and is the first to achieve the two complexity bounds simultaneously. The set of common tangents provides basic information about the convex hulls of the polygons-whether they are nested, overlapping, or disjoint-and our algorithm thus also decides this relationship.

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Section: Introductionmentioning

confidence: 99%

Common Tangents of Two Disjoint Polygons in Linear Time and Constant Workspace

Abrahamsen

Walczak

2018

ACM Trans. Algorithms

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“…We are on the cusp of the emergence of a new wave of nonvolatile memory technologies that are projected to become the dominant type of main memory in the near future [1, 2, 40,54]. A key property of these new memory technologies (e.g., phase-change memory, spin-torque transfer magnetic RAM, and memristor-based resistive RAM) is their asymmetric read-write costs: Writes can be an order of magnitude or more higher energy, higher latency, and lower (per-module) bandwidth than reads [3,8,11,12,15,22,23,32,33,36,46,52]. This high cost for writes motivates the design of models that reflect this asymmetry and "write-efficient" algorithms that perform well under such models by reducing their number of writes.…”

Section: Introductionmentioning

confidence: 99%

“…Our follow-on paper [11] presented write-efficient sequential algorithms for a number of fundamental problems, and defined the sequential (M, ω)-Asymmetric RAM model that combines a small symmetric-cost memory of size M with a large asymmetric-cost memory. Finally, Carson et al [15] recently presented a number of interesting results for models with asymmetric read-write costs. Specifically, they considered (i) sequential algorithms on a model with a small symmetric memory and a large asymmetric memory, both cache-oblivious and not, and (ii) parallel algorithms on a distributed memory model where the last level of the memory hierachy on each node has asymmetric read-write costs.…”

Section: Introductionmentioning

confidence: 99%

Parallel Algorithms for Asymmetric Read-Write Costs

Ben-David

Blelloch

Fineman

et al. 2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

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Motivated by the significantly higher cost of writing than reading in emerging memory technologies, we consider parallel algorithm design under such asymmetric read-write costs, with the goal of reducing the number of writes while preserving work-efficiency and low span. We present a nested-parallel model of computation that combines (i) small per-task stack-allocated memories with symmetric read-write costs and (ii) an unbounded heap-allocated shared memory with asymmetric read-write costs, and show how the costs in the model map efficiently onto a more concrete machine model under a work-stealing scheduler. We use the new model to design reduced-write, work-efficient, low-span parallel algorithms for a number of fundamental problems such as reduce, list contraction, tree contraction, breadth-first search, ordered filter, and planar convex hull. For the latter two problems, our algorithms are output-sensitive in that the work and number of writes decrease with the output size. We also present a reduced-write, low-span minimum spanning tree algorithm that is nearly work-efficient (off by the inverse Ackermann function). Our algorithms reveal several interesting techniques for significantly reducing shared memory writes in parallel algorithms without asymptotically increasing the number of shared memory reads.

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“…To obtain the retarded components of the scattering self-energies, the following relationship can be used: Σ R ≈ (Σ > − Σ < )/2, which is also valid for Π R[14]. Due to computational reasons, only the diagonal blocks of Σ R≷,S are retained, while N B non-diagonal connections are kept for Π R≷,S .The evaluation of Eqs (3)(4)(5). does not require the knowledge of all entries of the G and D matrices, but of two (lesser and greater) 5-D tensors of shape [N k z , N E , N A , N or b , N or b ] for electrons and two 6-D tensors of shape […”

mentioning

confidence: 99%

Optimizing the data movement in quantum transport simulations via data-centric parallel programming

Ziogas

Ben-Nun

Fernández

et al. 2019

Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis

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Designing efficient cooling systems for integrated circuits (ICs) relies on a deep understanding of the electro-thermal properties of transistors. To shed light on this issue in currently fabricated Fin-FETs, a quantum mechanical solver capable of revealing atomicallyresolved electron and phonon transport phenomena from firstprinciples is required. In this paper, we consider a global, datacentric view of a state-of-the-art quantum transport simulator to optimize its execution on supercomputers. The approach yields coarseand fine-grained data-movement characteristics, which are used for performance and communication modeling, communicationavoidance, and data-layout transformations. The transformations are tuned for the Piz Daint and Summit supercomputers, where each platform requires different caching and fusion strategies to perform optimally. The presented results make ab initio device simulation enter a new era, where nanostructures composed of over 10,000 atoms can be investigated at an unprecedented level of accuracy, paving the way for better heat management in next-generation ICs.

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Write-Avoiding Algorithms

Cited by 25 publications

References 26 publications

Common Tangents of Two Disjoint Polygons in Linear Time and Constant Workspace

Common Tangents of Two Disjoint Polygons in Linear Time and Constant Workspace

Parallel Algorithms for Asymmetric Read-Write Costs

Optimizing the data movement in quantum transport simulations via data-centric parallel programming

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