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An algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations

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Abstract

We present an algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations wherem is the number of constraints, andn is the number of variables. Each operation is performed to a precision of O(L) bits.L is bounded by the number of bits in the input. The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of\(\sqrt {m + n} \).

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References

  1. D.A. Bayer and J.C. Lagarias, “The non-linear geometry of linear programming I. Affine and projective scaling trajectories,”Transactions of the American Mathematical Society (1989), to appear.

  2. J. Edmonds, “Systems of distinct representatives and linear algebra,”Journal of Research of the National Bureau of Standards 71B (1967) 241–245.

    Google Scholar 

  3. F.R. Gantmacher,Matrix Theory, Vol. 1 (Chelsea, London, 1959) Chapter 2.

    Google Scholar 

  4. C. Gonzaga, “An algorithm for solving linear programming problems in O(n 3 L) operations,” Memorandum UCB/ERL M87/10, Electronics Research Laboratory, University of Berkeley (Berkeley, CA, 1987).

    Google Scholar 

  5. N. Karmarkar, “A new polynomial time algorithm for linear programming,”Combinatorica 4 (1984) 373–395.

    Google Scholar 

  6. L.G. Khachian, “Polynomial algorithms in linear programming,”Žurnal Vyčislitel'noî Matematiki i Matematičeskoî Fiziki 20 (1980) 53–72.

    Google Scholar 

  7. C. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, NJ, 1982).

    Google Scholar 

  8. J. Renegar, “A polynomial-time algorithm, based on Newton's method, for linear programming,”Mathematical Programming, 40 (1988) 59–93.

    Google Scholar 

  9. Gy. Sonnevand, “An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming,” preprint, Department of Numerical Analysis, Institute of Mathematics, Eötvös University (Budapest, 1989) 6–8.

    Google Scholar 

  10. G.W. Stewart,Introduction to Matrix Computations (Academic Press, New York, 1973).

    Google Scholar 

  11. P.M. Vaidya, “An algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations,”Proceedings 19th Annual ACM Symposium Theory of Computing (1987) 29–38.

  12. J.H. Wilkinson,The Algebraic Eigenvalue Problem (Oxford University Press (Clarendon), London and New York, 1965).

    Google Scholar 

  13. G. Zoutendijk,Mathematical Programming Methods (North-Holland, New York, 1976).

    Google Scholar 

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Authors and Affiliations

  1. AT&T Bell Laboratories, Murray Hill, 07974, NJ, USA

    Pravin M. Vaidya

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  1. Pravin M. Vaidya
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Vaidya, P.M. An algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations. Mathematical Programming 47, 175–201 (1990). https://doi.org/10.1007/BF01580859

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  • DOI: https://doi.org/10.1007/BF01580859

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