Approximation algorithms for low-distortion embeddings into low-dimensional spaces
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67767097-MIT.pdf
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1.27 MB
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131db1e917ed3a2db992380d13faae4b
Author(s)
Sidiropoulos, Anastasios
Advisor(s)
Piotr Indyk.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. We give an O([square root] n)-approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. For the same problem, we give an exact algorithm, with running-time exponential in the distortion. We complement these results by showing that the problem is NP-hard to [alpha]-approximate, for some constant [alpha] > 1. For the two-dimensional case, we show a O([square root] n) upper bound for the distortion required to embed an n-point subset of the two-dimensional sphere, into the plane. We prove that this bound is asymptotically tight, by exhibiting n-point subsets such that any embedding into the plane has distortion [omega]([square root] n). These techniques yield a O(1)-approximation algorithm for the problem of embedding an n-point subset of the sphere into the plane.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.
Includes bibliographical references (p. 33-35).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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