# Minimizing and Computing the Inverse Geodesic Length on Trees

@article{Gaspers2019MinimizingAC, title={Minimizing and Computing the Inverse Geodesic Length on Trees}, author={Serge Gaspers and Joshua Lau}, journal={ArXiv}, year={2019}, volume={abs/1811.03836} }

The inverse geodesic length (IGL) of a graph $G=(V,E)$ is the sum of inverse distances between every two vertices: $IGL(G) = \sum_{\{u,v\} \subseteq V} \frac{1}{d_G(u,v)}$. In the MinIGL problem, the input is a graph $G$, an integer $k$, and a target inverse geodesic length $T$, and the question is whether there are $k$ vertices whose deletion decreases the IGL of $G$ to at most $T$. Aziz et al. (2018) proved that MinIGL is $W[1]$-hard for parameter treewidth, but the complexity status of the…

## 2 Citations

Computing the Inverse Geodesic Length in Planar Graphs and Graphs of Bounded Treewidth

- MathematicsACM Trans. Algorithms
- 2022

The inverse geodesic length of a graph G is shown to be the sum of the inverse of the distances between all pairs of distinct vertices of G, known as the Harary index or the global efficiency of the graph.

Optimal Surveillance of Covert Networks by Minimizing Inverse Geodesic Length

- MathematicsAAAI
- 2019

It is shown that MINIGL-ED is fixed-parameter tractable for parameter T and vertex cover by modeling the problem as an integer quadratic program and FPT algorithms parameterized by twin cover and neighborhood diversity combined with the deletion budget k are provided.

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