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Duality between distant point and median of a tree network space

Published online by Cambridge University Press:  17 February 2009

D. K. Kulshrestha
D. K. Kulshrestha
Affiliation:
School of Mathematical Sciences, The Flinders University of South Australia.
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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 3 , January 1989 , pp. 304 - 312
Copyright
Copyright © Australian Mathematical Society 1989

References

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