MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
EMBEDDINGS TO RECTILINEAR SPACE AND GROMOV--HAUSDORFF DISTANCES
A. O. Ivanov, A. A. Tuzhilin

Abstract

We show that the problem whether a given finite metric space can be embedded into $m$-dimensional rectilinear space can be reformulated in terms of the Gromov--Hausdorff distance between some special finite metric spaces.

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Keywords: Gromov--Hausdorff distance; rectilinear space; isometric embeddings; finite metric spaces; normed spaces.

MSC: 46B85, 51F99, 53C23

DOI: 10.57016/MV-TU633QO3

Pages:  136$-$148     

Volume  76 ,  Issue  1-2 ,  2024