LOCAL VERSUS GLOBAL PROPERTIES OF METRIC SPACES
Sanjeev Arora, László Lovász, Ilan Newman, Yuval Rabani, Yuri G. Rabinovich, Santosh Vempala · 2006
Motivated by applications in combinatorial optimization, we study the extent to which the global properties of a metric space, and especially its embeddability into ℓ1 with low distortion, are determined by the properties of its small subspaces. We establish both upper and lower bounds on the distortion of embedding locally constrained metrics into various target spaces. Other aspects of locally constrained metrics are studied as well, in particular, how far are those metrics from general metrics.