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On a quadratic programming problem involving distances in trees

Author

Listed:
  • R. B. Bapat

    (Indian Statistical Institute)

  • S. K. Neogy

    (Indian Statistical Institute)

Abstract

Let $$T$$ T be a tree and let $$D$$ D be the distance matrix of the tree. The problem of finding the maximum of $$x'Dx$$ x ′ D x subject to $$x$$ x being a nonnegative vector with sum one occurs in many different contexts. These include some classical work on the transfinite diameter of a finite metric space, equilibrium points of symmetric bimatrix games and maximizing weighted average distance in graphs. We show that the problem can be converted into a strictly convex quadratic programming problem and hence it can be solved in polynomial time.

Suggested Citation

  • R. B. Bapat & S. K. Neogy, 2016. "On a quadratic programming problem involving distances in trees," Annals of Operations Research, Springer, vol. 243(1), pages 365-373, August.
    • Handle: RePEc:spr:annopr:v:243:y:2016:i:1:d:10.1007_s10479-014-1743-y
    DOI: 10.1007/s10479-014-1743-y
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    References listed on IDEAS

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    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    3. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
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