You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
CPU-SIMD GPU TPUs will be increasingly powerful. The algorithm using neural network and heterogeneous computing framework will bring significant performance improvement. In this paper we prove a novel neural network-based sorting algorithm, NNS which hold lower time complexity than @math and easy implement in heterogeneous framework executed by CPU and GPU. Our initial results show that our learned sorting algorithm can increases by @math X than std::sort(). More importantly, this work provides just a glimpse of using neural network to enhance or even replace classical algorithm and also the benefit of designing algorithm specifically for heterogeneous computing frameworks.

Cited Abstract(s):
[1]: Sorting is a kernel algorithm for a wide range of applications. We present a new algorithm, GPU-Warpsort, to perform comparison-based parallel sort on Graphics Processing Units (GPUs). It mainly consists of a bitonic sort followed by a merge sort. Our algorithm achieves high performance by efficiently mapping the sorting tasks to GPU architectures. Firstly, we take advantage of the synchronous execution of threads in a warp to eliminate the barriers in bitonic sorting network. We also provide sufficient homogeneous parallel operations for all the threads within a warp to avoid branch divergence. Furthermore, we implement the merge sort efficiently by assigning each warp independent pairs of sequences to be merged and by exploiting totally coalesced global memory accesses to eliminate the bandwidth bottleneck. Our experimental results indicate that GPU-Warpsort works well on different kinds of input distributions, and it achieves up to 30 higher performance than previous optimized comparison-based GPU sorting algorithm on input sequences with millions of elements.

[2]: We present the design of a sample sort algorithm for manycore GPUs. Despite being one of the most efficient comparison-based sorting algorithms for distributed memory architectures its performance on GPUs was previously unknown. For uniformly distributed keys our sample sort is at least 25 and on average 68 faster than the best comparison-based sorting algorithm, GPU Thrust merge sort, and on average more than 2 times faster than GPU quicksort. Moreover, for 64-bit integer keys it is at least 63 and on average 2 times faster than the highly optimized GPU Thrust radix sort that directly manipulates the binary representation of keys. Our implementation is robust to different distributions and entropy levels of keys and scales almost linearly with the input size. These results indicate that multi-way techniques in general and sample sort in particular achieve substantially better performance than two-way merge sort and quicksort.

[3]: We describe the design of high-performance parallel radix sort and merge sort routines for manycore GPUs, taking advantage of the full programmability offered by CUDA. Our radix sort is the fastest GPU sort and our merge sort is the fastest comparison-based sort reported in the literature. Our radix sort is up to 4 times faster than the graphics-based GPUSort and greater than 2 times faster than other CUDA-based radix sorts. It is also 23 faster, on average, than even a very carefully optimized multicore CPU sorting routine. To achieve this performance, we carefully design our algorithms to expose substantial fine-grained parallelism and decompose the computation into independent tasks that perform minimal global communication. We exploit the high-speed onchip shared memory provided by NVIDIA's GPU architecture and efficient data-parallel primitives, particularly parallel scan. While targeted at GPUs, these algorithms should also be well-suited for other manycore processors.

[4]:
The results of and [2] indicated that the radix sort algorithm of [1]0 outperforms both warp sort [1] and sample sort [1]2 , so the radix sort of GPU-radix2 is the fastest GPU sort algorithm for 32-bit integer keys.