On a quadratic programming problem involving distances in trees

R. B. Bapat () and S. K. Neogy ()
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R. B. Bapat: Indian Statistical Institute
S. K. Neogy: Indian Statistical Institute

Annals of Operations Research, 2016, vol. 243, issue 1, No 22, 365-373

Abstract: 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.

Keywords: Tree; Distance matrix; Quadratic programming problem; Finite metric space; Symmetric bimatrix game; Polynomial time; Lemke’s algorithm; 90C20; 05C05; 94C15 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10479-014-1743-y

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