• Corpus ID: 18292372

Up- and downgrading the 1-median in a network

@inproceedings{Gassner2008UpAD,
title={Up- and downgrading the 1-median in a network},
author={Elisabeth Gassner},
year={2008}
}
While classical location problems deal with finding optimal locations for facilities, the task of the corresponding upgrading (downgrading) version is to change the underlying network within certain bounds such that the optimal objective value that can be obtained in the modified network is as good (bad) as possible. In this paper we allow to change the vertex weights within given bounds such that a linear budget constraint is satisfied. For the upgrading 1-median problem an O(n) time algorithm…
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References

SHOWING 1-10 OF 35 REFERENCES
An Algorithmic Approach to Network Location Problems. II: The p-Medians
• Computer Science
• 1979
An algorithm is presented which finds a p-median of a tree (for $p > 1$) in time $O(n^2 \cdot p^2 )$.
Inverse median problems
• Mathematics
Discret. Optim.
• 2004
Approximation Algorithms for Certain Network Improvement Problems
• Computer Science
J. Comb. Optim.
• 1998
A brief overview of the models and definitions of the various problems considered are provided and several new results on the complexity and approximability of network improvement problems are presented.
A Network Improvement Problem Under Different Norms
• Mathematics, Computer Science
Comput. Optim. Appl.
• 2004
This paper considers a network improvement problem, called vertex-to-vertices distance reduction problem, and presents a strongly polynomial algorithm to solve the problem and shows that achieving an approximation ratio O(log(|V|)) is NP-hard.
A linear time algorithm for the reverse 1‐median problem on a cycle
• Mathematics
Networks
• 2006
This article deals with the reverse 1‐median problem on graphs with positive vertex weights. The problem is proved to be strongly NP‐hard even in the case of bipartite graphs and not approximable
Optimal Center Location in Simple Networks
In this paper, simple one-pass solution algorithms are given for two classes of topologically simple networks, namely those which are either acyclic or contain exactly one cycle.
Modifying Edges of a Network to Obtain Short Subgraphs
• Mathematics, Computer Science
Theor. Comput. Sci.
• 1998
Reverse 2-median problem on trees
• Mathematics
Discret. Appl. Math.
• 2008