Hardness of Embedding Metric Spaces of Equal Size

Abstract. We study the problem embedding an n-point metric space into another n-point metric space while minimizing distortion. We show that there is no polynomial time algorithm to approximate the minimum distortion within a factor of Ω((log n)1/4−δ ) for any constant δ > 0, unless NP ⊆ DTIME(npoly(log n)) ). We give a simple reduction from the METRIC LABELING problem which was shown to be inapproximable by Chuzhoy and Naor [10].

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Subhash Khot, Rishi Saket
• Keywords: Algorithms, APPROX 2007, METRIC LABELING Problem, N-point Metric Space, Polynomial Time Algorithm