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An O(n) algorithm for the multiple-choice knapsack linear program

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Abstract

An algorithm for solving the linear program associated with the multiple choice knapsack problem is described. The algorithm is shown to work in time linear in the number of variables. This improves the previously known best bound for this problem, and is optimal to within a constant factor.

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References

  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman,The design and analysis of Computer algorithms (Addison-Wesley, Reading, MA, 1974).

    MATH  Google Scholar 

  2. E. Balas and E. Zemel, An algorithm for large zero-one knapsack problems.Operations Research 28 (1980) 1132–1154

    Article  MathSciNet  Google Scholar 

  3. M.E. Dyer, A geometrical approach to two-constraint linear programs with generalised upper bounds, Research Report, Teesside Polytechnic (1981).

  4. M.E. Dyer, Two-variable linear programs are solvable in linear time, Research Report, Teesside Polytechnic (1981).

  5. F. Glover and D. Klingman, A O(n logn) algorihtm for LP knapsacks with GUB constraints,Mathematical Programming 17 (1979) 345–361.

    Article  MATH  MathSciNet  Google Scholar 

  6. T. Ibaraki, T. Hasegawa, K. Teranaka and J. Iwase, The multiple choice knapsack problem,Journal of the Operations Research Society of Japan 21 (1978) 59–95.

    MATH  MathSciNet  Google Scholar 

  7. R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, NJ, 1970).

    MATH  Google Scholar 

  8. P. Sinha and A. Zoltners, The multiple choice knapsack problem,Operations Research 27 (1979) 503–515.

    MATH  MathSciNet  Google Scholar 

  9. E. Zemel, The linear multiple choice knapsack problem,Operations Reseach 28 (1980) 1412–1423.

    MATH  MathSciNet  Google Scholar 

Additional references

  1. M.E. Dyer, Linear time algorithms for two and three variable linear programs,SIAM Journal on Computing, to appear.

  2. N. Megiddo, Linear-time algorithms for linear-programming in ℝ3 and related problems,Proceedings of 23rd IEEE Symposium on Foundations of Computer Science (1982), 329–338.

  3. N. Megiddo, Solving linear programming in linear time when the dimension is fixed, April 1982, submitted for publication.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Teesside Polytechnic, Middlesbrough, Cleveland, UK

    M. E. Dyer

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  1. M. E. Dyer
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Dyer, M.E. An O(n) algorithm for the multiple-choice knapsack linear program. Mathematical Programming 29, 57–63 (1984). https://doi.org/10.1007/BF02591729

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  • DOI: https://doi.org/10.1007/BF02591729

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