A face cover perspective to $\ell_1$ embeddings of planar graphs

21 Jul 2019 Filtser Arnold

It was conjectured by Gupta et al. [Combinatorica04] that every planar graph can be embedded into $\ell_1$ with constant distortion. However, given an $n$-vertex weighted planar graph, the best upper bound on the distortion is only $O(\sqrt{\log n})$, by Rao [SoCG99]... (read more)

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  • DATA STRUCTURES AND ALGORITHMS
  • COMPUTATIONAL GEOMETRY