theadana-porn.
Goemans and Linial conjectured that negative type metrics (metrics that are squares of Euclidean metrics) embed into L_1 with constant distortion. Negative type metrics arise naturally as solutions of semidefinite relaxations for Sparsest Cut and Graph Partitioning problems. The GL-conjecture implies that the "integrality ratio" for the SDP-relaxation is bounded by a constant (which gives constant factor approximation algorithm). The recent breakthrough algorithm of [Arora Rao Vazirani] gave O(\sqrt{log n}) upper bound on the integrality ratio and they too conjectured a constant upper bound.