License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2017.23
URN: urn:nbn:de:0030-drops-73769
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7376/
Go to the corresponding LIPIcs Volume Portal

Bury, Marc ; Schwiegelshohn, Chris

On Finding the Jaccard Center

pdf-format:
LIPIcs-ICALP-2017-23.pdf (0.5 MB)

Abstract

We initiate the study of finding the Jaccard center of a given collection N of sets. For two sets X,Y, the Jaccard index is defined as |X\cap Y|/|X\cup Y| and the corresponding distance is 1-|X\cap Y|/|X\cup Y|. The Jaccard center is a set C minimizing the maximum distance to any set of N.

We show that the problem is NP-hard to solve exactly, and that it admits a PTAS while no FPTAS can exist unless P = NP.
Furthermore, we show that the problem is fixed parameter tractable in the maximum Hamming norm between Jaccard center and any input set. Our algorithms are based on a compression technique similar in spirit to coresets for the Euclidean 1-center problem.

In addition, we also show that, contrary to the previously studied median problem by Chierichetti et al. (SODA 2010), the continuous version of the Jaccard center problem admits a simple polynomial time algorithm.

BibTeX - Entry

@InProceedings{bury_et_al:LIPIcs:2017:7376,
  author =	{Marc Bury and Chris Schwiegelshohn},
  title =	{{On Finding the Jaccard Center}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7376},
  URN =		{urn:nbn:de:0030-drops-73769},
  doi =		{10.4230/LIPIcs.ICALP.2017.23},
  annote =	{Keywords: Clustering, 1-Center, Jaccard}
}

Keywords: Clustering, 1-Center, Jaccard
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI