Topic

# Dynamic programming

About: Dynamic programming is a(n) research topic. Over the lifetime, 14128 publication(s) have been published within this topic receiving 369783 citation(s). The topic is also known as: dynamic optimization & DP.

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01 May 1995TL;DR: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization.

Abstract: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning.

10,491 citations

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NEC

^{1}TL;DR: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition, in which the warping function slope is restricted so as to improve discrimination between words in different categories.

Abstract: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition. First, a general principle of time-normalization is given using time-warping function. Then, two time-normalized distance definitions, called symmetric and asymmetric forms, are derived from the principle. These two forms are compared with each other through theoretical discussions and experimental studies. The symmetric form algorithm superiority is established. A new technique, called slope constraint, is successfully introduced, in which the warping function slope is restricted so as to improve discrimination between words in different categories. The effective slope constraint characteristic is qualitatively analyzed, and the optimum slope constraint condition is determined through experiments. The optimized algorithm is then extensively subjected to experimental comparison with various DP-algorithms, previously applied to spoken word recognition by different research groups. The experiment shows that the present algorithm gives no more than about two-thirds errors, even compared to the best conventional algorithm.

5,478 citations

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TL;DR: Sequence alignment methods often use something called a 'dynamic programming' algorithm, which can be a good idea or a bad idea, depending on the method used.

Abstract: Sequence alignment methods often use something called a 'dynamic programming' algorithm. What is dynamic programming and how does it work?

5,336 citations

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TL;DR: A new greedy alignment algorithm is introduced with particularly good performance and it is shown that it computes the same alignment as does a certain dynamic programming algorithm, while executing over 10 times faster on appropriate data.

Abstract: For aligning DNA sequences that differ only by sequencing errors, or by equivalent errors from other sources, a greedy algorithm can be much faster than traditional dynamic programming approaches and yet produce an alignment that is guaranteed to be theoretically optimal. We introduce a new greedy alignment algorithm with particularly good performance and show that it computes the same alignment as does a certain dynamic programming algorithm, while executing over 10 times faster on appropriate data. An implementation of this algorithm is currently used in a program that assembles the UniGene database at the National Center for Biotechnology Information.

4,111 citations

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01 Jan 1989

Abstract: I. THE RECURSIVE APPROACH 1. Introduction 2. An Overview 2.1 A Deterministic Model of Optimal Growth 2.2 A Stochastic Model of Optimal Growth 2.3 Competitive Equilibrium Growth 2.4 Conclusions and Plans II. DETERMINISTIC MODELS 3. Mathematical Preliminaries 3.1 Metric Spaces and Normed Vector Spaces 3.2 The Contraction Mapping Theorem 3.3 The Theorem of the Maximum 4. Dynamic Programming under Certainty 4.1 The Principle of Optimality 4.2 Bounded Returns 4.3 Constant Returns to Scale 4.4 Unbounded Returns 4.5 Euler Equations 5. Applications of Dynamic Programming under Certainty 5.1 The One-Sector Model of Optimal Growth 5.2 A "Cake-Eating" Problem 5.3 Optimal Growth with Linear Utility 5.4 Growth with Technical Progress 5.5 A Tree-Cutting Problem 5.6 Learning by Doing 5.7 Human Capital Accumulation 5.8 Growth with Human Capital 5.9 Investment with Convex Costs 5.10 Investment with Constant Returns 5.11 Recursive Preferences 5.12 Theory of the Consumer with Recursive Preferences 5.13 A Pareto Problem with Recursive Preferences 5.14 An (s, S) Inventory Problem 5.15 The Inventory Problem in Continuous Time 5.16 A Seller with Unknown Demand 5.17 A Consumption-Savings Problem 6. Deterministic Dynamics 6.1 One-Dimensional Examples 6.2 Global Stability: Liapounov Functions 6.3 Linear Systems and Linear Approximations 6.4 Euler Equations 6.5 Applications III. STOCHASTIC MODELS 7. Measure Theory and Integration 7.1 Measurable Spaces 7.2 Measures 7.3 Measurable Functions 7.4 Integration 7.5 Product Spaces 7.6 The Monotone Class Lemma

2,943 citations