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Necessary and Sufficient Conditions for Dynamic Programming of Combinatorial Type

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P. BonzonAuthors Info & Claims

Journal of the ACM (JACM), Volume 17, Issue 4

Pages 675 - 682

https://doi.org/10.1145/321607.321616

Published: 01 October 1970 Publication History

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Abstract

A general formulation of discrete deterministic dynamic programming is given. This definition is obtained formally by derivation of a simplified algorithm from a general algorithm, and gives simultaneously the class of concurrent problems.

References

[1]

BELLMAN, R. Dynamic Programming. Princeton U. Press, Princeton, N. J., 1957.

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ARIS, R. Discrete Dynamic Programming. Blaisdell, New York, 1964.

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NEMHAUSER, G. Introduction to Dynamic Programming. Wiley, New York, 1966.

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KARP, R. M., AND HELD, iM. Finite-state processes and dynamic programming. SIAM J. Appl. Math. 15, 3 (May 1967), 693-718.

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Cited By

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Wang YMary ASagot MSinaimeri B(2023)A General Framework for Enumerating Equivalence Classes of SolutionsAlgorithmica10.1007/s00453-023-01131-185:10(3003-3023)Online publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1007/s00453-023-01131-1
Xie CTravis Waller S(2012)Parametric search and problem decomposition for approximating Pareto-optimal pathsTransportation Research Part B: Methodological10.1016/j.trb.2012.03.00546:8(1043-1067)Online publication date: Sep-2012
https://doi.org/10.1016/j.trb.2012.03.005
Curtis S(1997)Dynamic programming: a different perspectiveAlgorithmic Languages and Calculi10.1007/978-0-387-35264-0_1(1-23)Online publication date: 1997
https://doi.org/10.1007/978-0-387-35264-0_1
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Index Terms

Necessary and Sufficient Conditions for Dynamic Programming of Combinatorial Type
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Design and analysis of algorithms
    1. Algorithm design techniques
      1. Dynamic programming

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Published In

Journal of the ACM Volume 17, Issue 4

Oct. 1970

169 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321607

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1970

Published in JACM Volume 17, Issue 4

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Wang YMary ASagot MSinaimeri B(2023)A General Framework for Enumerating Equivalence Classes of SolutionsAlgorithmica10.1007/s00453-023-01131-185:10(3003-3023)Online publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1007/s00453-023-01131-1
Xie CTravis Waller S(2012)Parametric search and problem decomposition for approximating Pareto-optimal pathsTransportation Research Part B: Methodological10.1016/j.trb.2012.03.00546:8(1043-1067)Online publication date: Sep-2012
https://doi.org/10.1016/j.trb.2012.03.005
Curtis S(1997)Dynamic programming: a different perspectiveAlgorithmic Languages and Calculi10.1007/978-0-387-35264-0_1(1-23)Online publication date: 1997
https://doi.org/10.1007/978-0-387-35264-0_1
Helman P(1986)The principle of optimality in the design of efficient algorithmsJournal of Mathematical Analysis and Applications10.1016/0022-247X(86)90147-2119:1-2(97-127)Online publication date: Oct-1986
https://doi.org/10.1016/0022-247X(86)90147-2
Lew A(1986)Richard Bellman's contributions to computer scienceJournal of Mathematical Analysis and Applications10.1016/0022-247X(86)90146-0119:1-2(90-96)Online publication date: Oct-1986
https://doi.org/10.1016/0022-247X(86)90146-0
Helman PRosenthal A(1985)A Comprehensive Model of Dynamic ProgrammingSIAM Journal on Algebraic and Discrete Methods10.1137/06060326:2(319-334)Online publication date: 1-Apr-1985
https://dl.acm.org/doi/10.1137/0606032
McEntire PLarson R(1981)Optimal Resource Allocation in Sparse NetworksIFAC Proceedings Volumes10.1016/S1474-6670(17)63681-414:2(1451-1456)Online publication date: Aug-1981
https://doi.org/10.1016/S1474-6670(17)63681-4
(1981)ReferencesIntroduction to Dynamic Programming10.1016/B978-0-08-025065-6.50016-4(287-288)Online publication date: 1981
https://doi.org/10.1016/B978-0-08-025065-6.50016-4
Mine HOhno KFukushima M(1976)Multilevel decomposition of nonlinear programming problems by dynamic programmingJournal of Mathematical Analysis and Applications10.1016/0022-247X(76)90141-453:1(7-27)Online publication date: Jan-1976
https://doi.org/10.1016/0022-247X(76)90141-4
Ibaraki T(1974)Classes of discrete optimization problems and their decision problemsJournal of Computer and System Sciences10.1016/S0022-0000(74)80024-38:1(84-116)Online publication date: 1-Feb-1974
https://dl.acm.org/doi/10.1016/S0022-0000%2874%2980024-3
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