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On linear programs with random costs

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Abstract

We consider linear programs in which the objective function (cost) coefficients are independent non-negative random variables, and give upper bounds for the random minimum cost. One application shows that for quadratic assignment problems with such costs certain branch-and-bound algorithms usually take more than exponential time.

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References

  1. R.E. Burkard, “Locations with spatial interactions—Quadratic assignment problem“, in: R.L. Francis and Mirchandani, eds.,Discrete location theory (Academic Press, New York, 1984).

    Google Scholar 

  2. R.E. Burkard and U. Fincke, “The asymptotic probabilistic behaviour of quadratic sum assignment problems“,Zeitschrift für Operations Research 27 (1983) 73–81.

    Google Scholar 

  3. A.M. Frieze, “Complexity of a 3-dimensional assignment problem“,European Journal of Operational Research 13 (1983) 161–164.

    Google Scholar 

  4. A.M. Frieze and J. Yadegar, “On the quadratic assignment problem“,Discrete Applied Mathematics 5 (1983) 89–98.

    Google Scholar 

  5. M.R. Garey and D. S. Johnson,Computers and intractability (Freeman, San Francisco, 1979).

    Google Scholar 

  6. W. Hoeffding, “Probability inequalities for sums of bounded random variables“,Journal of the American Statistical Association 58 (1963) 13–30.

    Google Scholar 

  7. R.M. Karp, Lecture at the NIHE Summer School on Combinatorial Optimisation, Dublin, 1983.

  8. C.J.H. McDiarmid, “On the greedy algorithm with random costs”, to appear.

  9. D.W. Walkup, “On the expected value of a random assignment problem“,SIAM Journal on Computing 8 (1979) 440–442.

    Google Scholar 

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Dyer, M.E., Frieze, A.M. & Mcdiarmid, C.J.H. On linear programs with random costs. Mathematical Programming 35, 3–16 (1986). https://doi.org/10.1007/BF01589437

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  • DOI: https://doi.org/10.1007/BF01589437

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