eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-11
36:1
36:21
10.4230/LIPIcs.APPROX/RANDOM.2020.36
article
Computing Bi-Lipschitz Outlier Embeddings into the Line
Chubarian, Karine
1
Sidiropoulos, Anastasios
2
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, IL, USA
Department of Computer Science, University of Illinois at Chicago, IL, USA
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(c²), where c denotes the optimal distortion [Bădoiu et al. 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol176-approx-random2020/LIPIcs.APPROX-RANDOM.2020.36/LIPIcs.APPROX-RANDOM.2020.36.pdf
metric embeddings
outliers
distortion
approximation algorithms