On a quadratic programming problem involving distances in trees

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

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Veröffentlicht in:Annals of operations research Jg. 243; H. 1-2; S. 365 - 373
Hauptverfasser: Bapat, R. B., Neogy, S. K.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2016
Springer
Springer Nature B.V
Schlagworte:
Business and Management
Combinatorics
Equilibrium
Game theory
Games
Graphs
Mathematical analysis
Mathematical research
Metric space
Operations research
Operations Research/Decision Theory
Polynomials
Quadratic programming
Texts
Theory of Computation
Trees
Trees (Graph theory)
Vectors (mathematics)
90C20
Quadratic programming problem
Finite metric space
94C15
Tree
Symmetric bimatrix game
Lemke’s algorithm
05C05
Distance matrix
Polynomial time
ISSN:0254-5330, 1572-9338
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Zusammenfassung:Let T be a tree and let D be the distance matrix of the tree. The problem of finding the maximum of x ′ D x 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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-014-1743-y