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May 2019 Computation of Inverse 1-Center Location Problem on the Weighted Trapezoid Graphs
Biswanath Jana, Sukumar Mondal, Madhumangal Pal
Missouri J. Math. Sci. 31(1): 14-35 (May 2019). DOI: 10.35834/mjms/1559181623

Abstract

Let $T_{TRP}$ be the tree corresponding to the weighted trapezoid graph $G=(V,E)$. The eccentricity $e(v)$ of the vertex $v$ is defined as the sum of the weights of the vertices from $v$ to the vertex farthest from $v \in T_{TRP}$. A vertex with minimum eccentricity in the tree $T_{TRP}$ is called the 1-center of that tree. In an inverse 1-center location problem, the parameter of the tree $T_{TRP}$ corresponding to the weighted trapezoid graph $G=(V,E)$, like vertex weights, have to be modified at minimum total cost such that a pre-specified vertex $s \in V$ becomes the 1-center of the trapezoid graph $G$. In this paper, we present an optimal algorithm to find an inverse 1-center location on the weighted tree $T_{TRP}$ corresponding to the weighted trapezoid graph $G=(V,E)$, where the vertex weights can be changed within certain bounds. The time complexity of our proposed algorithm is $O(n)$, where $n$ is the number of vertices of the trapezoid graph $G$.

Citation

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Biswanath Jana. Sukumar Mondal. Madhumangal Pal. "Computation of Inverse 1-Center Location Problem on the Weighted Trapezoid Graphs." Missouri J. Math. Sci. 31 (1) 14 - 35, May 2019. https://doi.org/10.35834/mjms/1559181623

Information

Published: May 2019
First available in Project Euclid: 30 May 2019

zbMATH: 07276110
MathSciNet: MR3960284
Digital Object Identifier: 10.35834/mjms/1559181623

Subjects:
Primary: 54A40

Rights: Copyright © 2019 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.31 • No. 1 • May 2019
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