Lower Bounds on Embeddings of Planar Graphs into the l1 Metric
نویسنده
چکیده
This paper presents an overview of existing bounds on l1-embeddings of planar metrics. A new family of graphs containing the K2,3 minor is introduced. Computational results on this family of graphs establish a new lower bound on the constant in the following conjecture: There exists an absolute constant Cmax > 0 such that every finite planar metric embeds into the l1 metric with distortion < Cmax. Analytical results establish an upper bound of 7/4 distortion on l1 embeddings of this family of graphs.
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