Open AccessInverse single facility location problem on a tree with balancing on the distance of server to clients
Author(s) -
Shahede Omidi,
Jafar Fathali
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021017
Subject(s) - bounded function , inverse , combinatorics , mathematics , enhanced data rates for gsm evolution , graph , tree (set theory) , discrete mathematics , computer science , geometry , mathematical analysis , telecommunications
We introduce a case of inverse single facility location problem on a tree where by minimum modifying in the length of edges, the difference of distances between the farthest and nearest clients to a given facility is minimized. Two cases are considered: bounded and unbounded nonnegative edge lengths. In the unbounded case, we show the problem can be reduced to solve the problem on a star graph. Then an \begin{document}$ O(nlogn) $\end{document} algorithm is developed to find the optimal solution. For the bounded edge lengths case an algorithm with time complexity \begin{document}$ O(n^2) $\end{document} is presented.