67,241 research outputs found
A lower bound for metric 1-median selection
Consider the problem of finding a point in an n-point metric space with the
minimum average distance to all points. We show that this problem has no
deterministic -query -approximation algorithms
Fast Clustering with Lower Bounds: No Customer too Far, No Shop too Small
We study the \LowerBoundedCenter (\lbc) problem, which is a clustering
problem that can be viewed as a variant of the \kCenter problem. In the \lbc
problem, we are given a set of points P in a metric space and a lower bound
\lambda, and the goal is to select a set C \subseteq P of centers and an
assignment that maps each point in P to a center of C such that each center of
C is assigned at least \lambda points. The price of an assignment is the
maximum distance between a point and the center it is assigned to, and the goal
is to find a set of centers and an assignment of minimum price. We give a
constant factor approximation algorithm for the \lbc problem that runs in O(n
\log n) time when the input points lie in the d-dimensional Euclidean space
R^d, where d is a constant. We also prove that this problem cannot be
approximated within a factor of 1.8-\epsilon unless P = \NP even if the input
points are points in the Euclidean plane R^2.Comment: 14 page
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