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 -