A Dynamic Programming Approach to Sequencing Problems

Previous article Next article A Dynamic Programming Approach to Sequencing ProblemsMichael Held and Richard M. KarpMichael Held and Richard M. Karphttps://doi.org/10.1137/0110015PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. L. Ackoff, Progress in Operations Research, Vol. I, Publications in Operations Research, No. 5, John Wiley & Sons Inc., New York, 1961xii+505 MR0121239 Google Scholar[2A] Richard Bellman, Combinatorial processes and dynamic programmingProc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, 217–249 MR0113718 0096.14506 CrossrefGoogle Scholar[2B] Richard Bellman, Dynamic programming treatment of the travelling salesman problem, J. Assoc. Comput. Mach., 9 (1962), 61–63 MR0135702 0106.14102 CrossrefISIGoogle Scholar[3] G. A. Croes, A method for solving traveling-salesman problems, Operations Res., 6 (1958), 791–812 MR0099887 CrossrefISIGoogle Scholar[4A] G. Dantzig, , R. Fulkerson and , S. Johnson, Solution of a large-scale traveling-salesman problem, J. Operations Res. Soc. Amer., 2 (1954), 393–410 MR0070932 CrossrefISIGoogle Scholar[4B] G. B. Dantzig, , D. R. Fulkerson and , S. M. Johnson, On a linear-programming, combinatorial approach to the traveling-salesman problem, Operations Res., 7 (1959), 58–66 MR0101823 CrossrefISIGoogle Scholar[5] Kurt Eisemann, The trim problem, Management Sci., 3 (1957), 279–284 MR0088407 0995.92500 CrossrefISIGoogle Scholar[6] Merrill M. Flood, The traveling-salesman problem, Operations Res., 4 (1956), 61–75 MR0078639 CrossrefISIGoogle Scholar[7] P. C. Gilmore and , R. E. Gomory, A linear programming approach to the cutting-stock problem, Operations Res., 9 (1961), 849–859 MR0137589 0096.35501 CrossrefISIGoogle Scholar[8] Maurice Kraitchik, Mathematical recreations, Dover Publications Inc., New York, N. Y., 1953, 330–, Chapter 11 MR0052446 0050.00901 Google Scholar[9] Robert McNaughton, Scheduling with deadlines and loss functions, Management Sci., 6 (1959/1960), 1–12 MR0110585 1047.90504 CrossrefISIGoogle Scholar[10] M. E. Salveson, The assembly line balancing problem, Journal of Industrial Engineering, 6 (1955), 18–25 Google Scholar[11] B. L. van der Waerden, Modern Algebra. Vol. I, Frederick Ungar Publishing Co., New York, N. Y., 1949xii+264 MR0029363 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Approximation Limitations of Pure Dynamic ProgrammingStasys Jukna and Hannes Seiwert18 February 2020 | SIAM Journal on Computing, Vol. 49, No. 1AbstractPDF (676 KB)On the Fine-Grained Complexity of Rainbow ColoringŁukasz Kowalik, Juho Lauri, and Arkadiusz Socała17 July 2018 | SIAM Journal on Discrete Mathematics, Vol. 32, No. 3AbstractPDF (640 KB)Bounding the Running Time of Algorithms for Scheduling and Packing ProblemsK. Jansen, F. Land, and K. 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