On a quadratic programming problem involving distances in trees

Article Type

Research Article

Publication Title

Annals of Operations Research

Abstract

Let T be a tree and let D be the distance matrix of the tree. The problem of finding the maximum of x′Dx subject to 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.

First Page

365

Last Page

373

DOI

10.1007/s10479-014-1743-y

Publication Date

8-1-2016

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