Coresets for weighted facilities and their applications

Dan Feldman, Amos Fiat, Micha Sharif

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We develop efficient (1 + ε)-approximation algorithms for generalized facility location problems. Such facilities are not restricted to being points in ℝd, and can represent more complex structures such as linear facilities (lines in ℝd, j-dimensional flats), etc. We introduce coresetsfor weighted (point) facilities. These prove to be useful for such generalized facility location problems, and provide efficient algorithms for their construction. Applications include: k-mean and k-median generalizations, i.e., find k lines that minimize the sum (or sum of squares) of the distances from each input point to its nearest line. Other applications are generalizations of linear regression problems to multiple regression lines, new SVD/PCA generalizations, and many more. The results significantly improve on previous work, which deals efficiently only with special cases. Open source code for the algorithms in this paper is also available.

Original languageEnglish
Title of host publication47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006
Pages315-324
Number of pages10
DOIs
StatePublished - 2006
Externally publishedYes
Event47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006 - Berkeley, CA, United States
Duration: 21 Oct 200624 Oct 2006

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006
Country/TerritoryUnited States
CityBerkeley, CA
Period21/10/0624/10/06

ASJC Scopus subject areas

  • Engineering (all)

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