@techreport{Rieger93,
TITLE = {Proximity in arrangements of algebraic sets},
AUTHOR = {Rieger, Joachim},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1996-1-003},
NUMBER = {MPI-I-1996-1-003},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {1996},
DATE = {1996},
ABSTRACT = {Let $X$ be an arrangement of $n$ algebraic sets $X_i$ in $d$-space, where the $X_i$ are either parameterized or zero-sets of dimension $0\le m_i\le d-1$. We study a number of decompositions of $d$-space into connected regions in which the distance-squared function to $X$ has certain invariances. These decompositions can be used in the following of proximity problems: given some point, find the $k$ nearest sets $X_i$ in the arrangement, find the nearest point in $X$ or (assuming that $X$ is compact) find the farthest point in $X$ and hence the smallest enclosing $(d-1)$-sphere. We give bounds on the complexity of the decompositions in terms of $n$, $d$, and the degrees and dimensions of the algebraic sets $X_i$.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}