## Dynamic Programming: a different perspective (1997)

Venue: | Algorithmic Languages and Calculi |

Citations: | 5 - 0 self |

### BibTeX

@INPROCEEDINGS{Curtis97dynamicprogramming:,

author = {Sharon Curtis},

title = {Dynamic Programming: a different perspective},

booktitle = {Algorithmic Languages and Calculi},

year = {1997},

pages = {1--23},

publisher = {Chapman & Hall}

}

### OpenURL

### Abstract

Dynamic programming has long been used as an algorithm design technique, with various mathematical theories proposed to model it. Here we take a different perspective, using a relational calculus to model the problems and solutions using dynamic programming. This approach serves to shed new light on the different styles of dynamic programming, representing them by different search strategies of the tree-like space of partial solutions. 1 INTRODUCTION AND HISTORY Dynamic programming is an algorithm design technique for solving many different types of optimization problem, applicable to such diverse fields as operations research (Ecker and Kupferschmid, 1988) and neutron transport theory (Bellman, Kagiwada and Kalaba, 1967). The mathematical theory of the subject dates back to 1957, when Richard Bellman (Bellman, 1957) first popularized the idea, producing a mathematical theory to model multi-stage decision processes and to solve related optimization problems. He was also the first to i...

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Citation Context ... operations research (Ecker and Kupferschmid, 1988) and neutron transport theory (Bellman, Kagiwada and Kalaba, 1967). The mathematical theory of the subject dates back to 1957, when Richard Bellman (=-=Bellman, 1957-=-) first popularized the idea, producing a mathematical theory to model multi-stage decision processes and to solve related optimization problems. He was also the first to introduce the idea of the Pri... |

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Citation Context ...istory of decisions made, whereas our partial solutions are more general, and can contain this information and more; also they can use more general datatypes than strings and other initial datatypes (=-=Malcolm, 1990-=-). The straightforward implementation of the specification would involve generating all 8 the leaves of the tree from the input. In order to consider how we might reduce the amount of computation, we ... |

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Citation Context ...or Levenshtein distance (see Levenshtein, 1966, or Wagner and Fischer, 1974) between the two strings, and this can be used for spell-checking, speech recognition, and comparison of DNA sequences (see =-=Galil and Giancarlo, 1989-=-) for example. Sankoff and Kruskal's book (1983) is the comprehensive reference on the subject. We will consider the following edit operations on strings: adding, deleting, or retaining a character. I... |

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Citation Context ...ns. 1 INTRODUCTION AND HISTORY Dynamic programming is an algorithm design technique for solving many different types of optimization problem, applicable to such diverse fields as operations research (=-=Ecker and Kupferschmid, 1988-=-) and neutron transport theory (Bellman, Kagiwada and Kalaba, 1967). The mathematical theory of the subject dates back to 1957, when Richard Bellman (Bellman, 1957) first popularized the idea, produci... |

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Citation Context ...(1982) presented more recent work on this, connecting it to the Principle of Optimality. Also, in line with recent trends concerning data structures, Helman (Helman and Rosenthal, 1985; Helman, 1986; =-=Helman, 1989-=-) has reworked traditional dynamic programming using trees rather than just strings, and specifically separating the ideas of problem structure and computation. Further work by de Moor (de Moor, 1992;... |

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Citation Context ...cently, Morin (1982) presented more recent work on this, connecting it to the Principle of Optimality. Also, in line with recent trends concerning data structures, Helman (Helman and Rosenthal, 1985; =-=Helman, 1986-=-; Helman, 1989) has reworked traditional dynamic programming using trees rather than just strings, and specifically separating the ideas of problem structure and computation. Further work by de Moor (... |

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Citation Context ...61), and further extended to sequential decision processes (discrete decision processes with an added cost structure imposed) by Karp, Held and others (Karp and Held, 1962 and 1967; Elmaghraby, 1970; =-=Ibaraki, 1973-=-). These structures model the problem itself, then the solution is obtained by checking that the principle of optimality applies, and producing the relevant functional equation, a recursion equation g... |

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Citation Context ...e subproblem twice. The method of performing the computation is little addressed in the early literature, although Bonzon did explore a particular theory for executing particular types of tabulation (=-=Bonzon, 1970-=-). More recent research has considered the method of computation more fully, and also The lim Model 3 alternative formulations of the Principle of Optimality. Mitten (1964) considered a Monotonicity A... |

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Citation Context ...ta by Shreider (1961), and further extended to sequential decision processes (discrete decision processes with an added cost structure imposed) by Karp, Held and others (Karp and Held, 1962 and 1967; =-=Elmaghraby, 1970-=-; Ibaraki, 1973). These structures model the problem itself, then the solution is obtained by checking that the principle of optimality applies, and producing the relevant functional equation, a recur... |

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