Bounds on distortion If original distance is not a metric, it is advisable to embed into a metric distance However, if does not obey relaxed metric properties, then this embedding cannot be low distortion Relaxed metric properties:   -relaxed symmetry:   -relaxed triangular inequality: If does not obey -relaxed symmetry, then any embedding into a metric space must have a distortion of at least than where If does not obey -relaxed triangular inequality, then any embedding into a metric space must have a distortion of at least