Computing Bi-Lipschitz Outlier Embeddings into the Line

02/24/2020
by   Karine Chubarian, et al.
0

The problem of computing a bi-Lipschitz embedding of a graphical metric into the line with minimum distortion has received a lot of attention. The best-known approximation algorithm computes an embedding with distortion O(c^2), where c denotes the optimal distortion [Bădoiu  2005]. We present a bi-criteria approximation algorithm that extends the above results to the setting of outliers. Specifically, we say that a metric space (X,ρ) admits a (k,c)-embedding if there exists K⊂ X, with |K|=k, such that (X∖ K, ρ) admits an embedding into the line with distortion at most c. Given k≥ 0, and a metric space that admits a (k,c)-embedding, for some c≥ 1, our algorithm computes a (poly(k, c, log n), poly(c))-embedding in polynomial time. This is the first algorithmic result for outlier bi-Lipschitz embeddings. Prior to our work, comparable outlier embeddings where known only for the case of additive distortion.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset