dc.contributor.author | Indyk, Piotr | |
dc.contributor.author | Wagner, Tal | |
dc.date.accessioned | 2018-05-11T14:06:29Z | |
dc.date.available | 2018-05-11T14:06:29Z | |
dc.date.issued | 2017-01 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/115312 | |
dc.description.abstract | he metric sketching problem is defined as follows. Given a metric on n points, and ϵ > 0, we wish to produce a small size data structure (sketch) that, given any pair of point indices, recovers the distance between the points up to a 1 + ϵ distortion. In this paper we consider metrics induced by l2 and l1 norms whose spread (the ratio of the diameter to the closest pair distance) is bounded by Φ > 0. A well-known dimensionality reduction theorem due to Johnson and Lindenstrauss yields a sketch of size O(ϵ[superscript −2] log(Φn)n log n), i.e., O(ϵ[superscript −2[] log(Φn)n log n) bits per point. We show that this bound is not optimal, and can be substantially improved to O(ϵ[superscript −2] log(1/ϵ) · log n + log log Φ) bits per point. Furthermore, we show that our bound is tight up to a factor of log(1/ϵ).
We also consider sketching of general metrics and provide a sketch of size O(n log(1/ϵ) + log log Φ) bits per point, which we show is optimal. | en_US |
dc.language.iso | en_US | |
dc.publisher | Association for Computing Machinery | en_US |
dc.relation.isversionof | http://dl.acm.org/citation.cfm?id=3039731 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | arXiv | en_US |
dc.title | Near-optimal (euclidean) metric compression | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Indyk, Piotr and Tal Wagner. "Near-optimal (euclidean) metric compression." SODA '17 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 16-19 September, 2017, Barcelona, Spain, Association for Computing Machinery, 2017. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.mitauthor | Indyk, Piotr | |
dc.contributor.mitauthor | Wagner, Tal | |
dc.relation.journal | SODA '17 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms | en_US |
dc.eprint.version | Original manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/ConferencePaper | en_US |
eprint.status | http://purl.org/eprint/status/NonPeerReviewed | en_US |
dspace.orderedauthors | Indyk, Piotr; Wagner, Tal | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-7983-9524 | |
dc.identifier.orcid | https://orcid.org/0000-0002-9455-6864 | |
mit.license | OPEN_ACCESS_POLICY | en_US |