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Probabilistic Metric Embedding via Metric Labeling

Authors Kamesh Munagala, Govind S. Sankar, Erin Taylor

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ACM Subject Classification
  • Theory of computation → Random projections and metric embeddings
Keywords
  • Metric Embedding
  • Approximation Algorithms
  • Ultrametrics

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Abstract

We consider probabilistic embedding of metric spaces into ultra-metrics (or equivalently to a constant factor, into hierarchically separated trees) to minimize the expected distortion of any pairwise distance. Such embeddings have been widely used in network design and online algorithms. Our main result is a polynomial time algorithm that approximates the optimal distortion on any instance to within a constant factor. We achieve this via a novel LP formulation that reduces this problem to a probabilistic version of uniform metric labeling.

Cite As Get BibTex

Kamesh Munagala, Govind S. Sankar, and Erin Taylor. Probabilistic Metric Embedding via Metric Labeling. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.2

Author Details

Kamesh Munagala
  • Department of Computer Science, Duke University, Durham, NC, USA
Govind S. Sankar
  • Department of Computer Science, Duke University, Durham, NC, USA
Erin Taylor
  • Department of Computer Science, Duke University, Durham, NC, USA

Funding

This work is supported by NSF grant CCF-2113798.

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