On the Inapproximability of Finding Minimum Monitoring Edge-Geodetic Sets
CoRR(2024)
Abstract
Given an undirected connected graph G = (V(G), E(G)) on n vertices, the
minimum Monitoring Edge-Geodetic Set (MEG-set) problem asks to find a subset M
⊆ V(G) of minimum cardinality such that, for every edge e ∈ E(G),
there exist x,y ∈ M for which all shortest paths between x and y in G
traverse e.
We show that, for any constant c < 1/2, no polynomial-time (c log
n)-approximation algorithm for the minimum MEG-set problem exists, unless
𝖯 = 𝖭𝖯.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined