文章基本信息

标题：Constant-Distortion Embeddings of Hausdorff Metrics into Constant-Dimensional l_p Spaces
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作者：Arturs Backurs ; Anastasios Sidiropoulos
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：60
页码：1:1-1:15
DOI：10.4230/LIPIcs.APPROX-RANDOM.2016.1
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We show that the Hausdorff metric over constant-size pointsets in constant-dimensional Euclidean space admits an embedding into constant-dimensional l_{infinity} space with constant distortion. More specifically for any s,d>=1, we obtain an embedding of the Hausdorff metric over pointsets of size s in d-dimensional Euclidean space, into l_{\infinity}^{s^{O(s+d)}} with distortion s^{O(s+d)}. We remark that any metric space M admits an isometric embedding into l_{infinity} with dimension proportional to the size of M. In contrast, we obtain an embedding of a space of infinite size into constant-dimensional l_{infinity}. We further improve the distortion and dimension trade-offs by considering probabilistic embeddings of the snowflake version of the Hausdorff metric. For the case of pointsets of size s in the real line of bounded resolution, we obtain a probabilistic embedding into l_1^{O(s*log(s()} with distortion O(s).
关键词：metric embeddings; Hausdorff metric; distortion; dimension