Abstract
We present in this chapter two necessary conditions for L 1-embeddability, namely, the hypermetric and the negative type conditions. There are many other known necessary conditions, arising from the known valid inequalities for the cut cone; they will be described in Part V. We focus here on the hypermetric and negative type conditions. These conditions seem indeed to be among the most essential ones. For instance, there are several classes of distance spaces for which these conditions are also sufficient for ensuring L 1-embeddability; see, in particular, Chapters 8, 19, 24, and Remark 6.3.5 for a summary. Hypermetric inequalities will be treated in detail for their own sake in Part II and, as facets of the cut cone, in Chapter 28.
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© 1997 Springer-Verlag Berlin Heidelberg
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Deza, M.M., Laurent, M. (1997). Conditions for L 1-Embeddability. In: Geometry of Cuts and Metrics. Algorithms and Combinatorics, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04295-9_6
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DOI: https://doi.org/10.1007/978-3-642-04295-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04294-2
Online ISBN: 978-3-642-04295-9
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