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Duality between distant point and median of a tree network space
Published online by Cambridge University Press: 17 February 2009
Abstract
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A point on a tree network space is said to be a distant point if it maximises its minimum weighted distance from any of its vertices. The median minimises the sum of its weighted distances from the vertices. In this paper two constrained problems are discussed. The first problem is to maximise the minimum of the weighted distances from the vertices subject to an upper bound value of the sum of the weighted distances from the vertices, while the second problem is to minimise the sum of the weighted distances subject to a lower bound value of the minimum weighted distance to any of its vertices. It is shown that these two constrained problems are duals of each other in a well defined sense.
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- Copyright © Australian Mathematical Society 1989
References
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