Non-Serial Dynamic Programming — A Survey

Esogbue, Augustine O.; Marks, Barry R.

doi:10.1057/jors.1974.43

Cited by 16 publications

(2 citation statements)

References 28 publications

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“…Karp and Held [16] concentrate on the sequential nature of dynamic programming. Non-serial dynamic programming is introduced later, among others, by Bertelè and Brioschi [3,12]. Helman [14] formalizes a wider view of dynamic programming based on the idea of computationally feasible dominance relations.…”

Section: Introductionmentioning

confidence: 99%

Sufficient and necessary conditions for solution finding in valuation-based systems

Roca-Lacostena

Cerquides

Pouly

2019

International Journal of Approximate Reasoning

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Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to linear equation systems.Many widely used dynamic programming algorithms for optimization problems rely on low treewidth decompositions and can be understood as particular cases of a single algorithmic scheme for finding solutions in a valuation algebra. The most encompassing description of this algorithmic scheme to date has been proposed by Pouly and Kohlas together with sufficient conditions for its correctness. Unfortunately, the formalization relies on a theorem for which we provide counterexamples. In spite of that, the mainline of Pouly and Kohlas' theory is correct, although some of the necessary conditions have to be revised. In this paper we analyze the impact that the counter-examples have on the theory, and rebuild the theory providing correct sufficient conditions for the algorithms. Furthermore, we also provide necessary conditions for the algorithms, allowing for a sharper characterization of when the algorithmic scheme can be applied.

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Section: Introductionmentioning

confidence: 99%

Sufficient and necessary conditions for solution finding in valuation-based systems

Roca-Lacostena

Cerquides

Pouly

2019

International Journal of Approximate Reasoning

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“…and d) fuzzy processes [2]. These researchers concentrated mainly on the non-serial dynamic programming.…”

Section: Introductionmentioning

confidence: 99%

The Usefulness of Dynamic Programming in Course Allocation in the Nigerian Universities

Amuji¹,

Ugwuanyim²,

Ogbonna³

et al. 2017

OJOp

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Having lectured in some universities and polytechnics in Nigeria, the researchers observed problems in course allocations. There are no lay-down techniques on how courses should be allocated with respect to the minimum and maximum credit a lecturer should carry in a semester. Many lecturers were overloaded while others were under-loaded. For this reason, dynamic programming model was developed for allocating courses among lecturers in the Nigerian universities using the Department of Statistics, Federal University of Technology Owerri, as a case study. From our analysis, we observed that among all the optimal allocations discovered in the study, the best optimal allocation policy was achieved at the point (1, 2, 1, 2). Allocation of courses in this order will yield an optimal credit hour of 12 per lecturer per semester.

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Dynamic Programming: Introductory Concepts

Sniedovich

2011

Wiley Encyclopedia of Operations Research and Management Science

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Dynamic programming (DP) is a general purpose problem solving methodology based on problem decomposition. The idea is to decompose a “difficult” problem into a family of “related problems”—which are often, but not always, “easier” subproblems of the “difficult” problem. Its plan of attack is then to embed the “difficult” problem of interest—the target problem—in a family of modified problems, and to use a functional equation to relate the solutions to these modified problems to one another. The solution obtained for this functional equation yields the solution to the modified problems as well as to the target problem. This approach has an extremely wide scope of application, but in operations research, DP is used primarily as a framework for the modeling, analysis, and, solution of optimization problems. The evolution of DP has entrenched the convention that DP treats problems as sequential decision problems. This fact is reflected in the DP terminology, notably in the central roles that the concepts “state” and “state transition” play in the theory. The subtle modeling issues associated with this approach have earned DP its reputation (perhaps notoriety) of being an “art.” Although DP's scope of operation is extremely wide‐ranging, in practice its use is often hampered by the curse of dimensionality. This difficulty has spawned the development of a host of methods and techniques aimed at dealing with the computational aspects of DP. This ongoing effort provides challenges and opportunities, especially in the development of general‐purpose DP software.

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Non-Serial Dynamic Programming — A Survey

Cited by 16 publications

References 28 publications

Sufficient and necessary conditions for solution finding in valuation-based systems

Sufficient and necessary conditions for solution finding in valuation-based systems

The Usefulness of Dynamic Programming in Course Allocation in the Nigerian Universities

Dynamic Programming: Introductory Concepts

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