An introduction to parallel dynamic programming

Gengler, Marc

doi:10.1007/bfb0027119

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…Byrd et al [31,30] and Smith and Schnabel [115] have developed several parallel implementations of the clustering method. Parallelization of classical paradigms have also been explored: parallel dynamic programming [63], branch and bound [26,45], tabu search, simulated annealing, and genetic algorithms [109]. In the paper of Clementi, Rolim, and Urland [37], randomized parallel algorithms are studied for shortest paths, maximum flows, maximum independent set, and matching problems.…”

Section: Parallel Optimizationmentioning

confidence: 99%

High Performance Optimization at the Door of the Exascale

Tadonki

2021

Preprint

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The next frontier of high performance computing is the Exascale, and this will certainly stand as a noteworthy step in the quest for processing speed potential. In fact, we always get a fraction of the technically available computing power (so-called theoretical peak), and the gap is likely to go hand-to-hand with the hardware complexity of the target system. Among the key aspects of this complexity, we have: the heterogeneity of the computing units, the memory hierarchy and partitioning including the non-uniform memory access (NUMA) configuration, and the interconnect for data exchanges among the computing nodes. Scientific investigations and cutting-edge technical activities should ideally scale-up with respect to sustained performance. The special case of quantitative approaches for solving (large-scale) problems deserves a special focus. Indeed, most of common real-life problems, even when considering the artificial intelligence paradigm, rely on optimization techniques for the main kernels of algorithmic solutions. Mathematical programming and pure combinatorial methods are not easy to implement efficiently on large-scale supercomputers because of irregular control flow, complex memory access patterns, heterogeneous kernels, numerical issues, to name a few. We describe and examine our thoughts from the standpoint of large-scale supercomputers.

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Section: Parallel Optimizationmentioning

confidence: 99%

High Performance Optimization at the Door of the Exascale

Tadonki

2021

Preprint

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“…PRAM algorithms for the string editing problem have been proposed by Apostolico et al [1]. A general study of parallel algorithms for dynamic programming can be found in [7].…”

Section: Introductionmentioning

confidence: 99%

Parallel dynamic programming for solving the string editing problem on a CGM/BSP

Alves¹,

Cáceres

Dehne

2002

Proceedings of the Fourteenth Annual ACM Symposium on Parallel Algorithms and Architectures

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In this paper we present a coarse-grained parallel algorithm for solving the string edit distance problem for a string A and all substrings of a string C. Our method is based on a novel CGM/BSP parallel dynamic programming technique for computing all highest scoring paths in a weighted grid graph. The algorithm requires log p rounds/supersteps and O( n 2 p log m) local computation, where p is the number of processors, p 2 ≤ m ≤ n. To our knowledge, this is the first efficient CGM/BSP algorithm for the alignment of all substrings of C with A. Furthermore, the CGM/BSP parallel dynamic programming technique presented is of interest in its own right and we expect it to lead to other parallel dynamic programming methods for the CGM/BSP.

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“…Dynamic programming algorithms that parallelise computations at each time step, but operate sequentially, are provided in [11], [12] for discrete states, and in [13] for the Riccati recursion in linear quadratic problems. Another approach to speed up computations for model predictive control (MPC) in linear quadratic problems is partial condensing [14], [15], which is based on splitting the problem into temporal blocks and eliminating the intermediate states algebraically.…”

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confidence: 99%

Temporal Parallelization of Dynamic Programming and Linear Quadratic Control

Särkkä

García-Fernández

2023

IEEE Trans. Automat. Contr.

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This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with logarithmic time complexity rather than linear time complexity. We apply this methodology to problems with finite state and control spaces, linear quadratic tracking control problems, and to a class of nonlinear control problems. The computational benefits of the parallel methods are demonstrated via numerical simulations run on a graphics processing unit.

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An introduction to parallel dynamic programming

Cited by 5 publications

References 15 publications

High Performance Optimization at the Door of the Exascale

High Performance Optimization at the Door of the Exascale

Parallel dynamic programming for solving the string editing problem on a CGM/BSP

Temporal Parallelization of Dynamic Programming and Linear Quadratic Control

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