TY - GEN

T1 - Coresets for weighted facilities and their applications

AU - Feldman, Dan

AU - Fiat, Amos

AU - Sharif, Micha

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35348851254&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2006.22

DO - 10.1109/FOCS.2006.22

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AN - SCOPUS:35348851254

SN - 0769527205

SN - 9780769527208

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 315

EP - 324

BT - 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006

T2 - 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006

Y2 - 21 October 2006 through 24 October 2006

ER -