Sparse Hop Spanners for Unit Disk Graphs

@article{Dumitrescu2020SparseHS,
  title={Sparse Hop Spanners for Unit Disk Graphs},
  author={Adrian Dumitrescu and Anirban Ghosh and Csaba D. T'oth},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.07840}
}
A unit disk graph $G$ on a given set of points $P$ in the plane is a geometric graph where an edge exists between two points $p,q \in P$ if and only if $|pq| \leq 1$. A subgraph $G'$ of $G$ is a $k$-hop spanner if and only if for every edge $pq\in G$, the topological shortest path between $p,q$ in $G'$ has at most $k$ edges. We obtain the following results for unit disk graphs. (i) Every $n$-vertex unit disk graph has a $5$-hop spanner with at most $5.5n$ edges. We analyze the family of… 

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