Region-restricted clustering for geographic data mining
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Region-restricted clustering for geographic data mining
Computational Geometry: Theory and Applications
Graph Drawing
Enclosing weighted points with an almost-unit ball
Information Processing Letters
New constructions of SSPDs and their applications
Proceedings of the twenty-sixth annual symposium on Computational geometry
A unified approach to approximate proximity searching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximate bregman near neighbors in sublinear time: beyond the triangle inequality
Proceedings of the twenty-eighth annual symposium on Computational geometry
Density index and proximity search in large graphs
Proceedings of the 21st ACM international conference on Information and knowledge management
Net and prune: a linear time algorithm for euclidean distance problems
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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For a set $P$ of $n$ points in the plane and an integer $k \leq n$, consider the problem of finding the smallest circle enclosing at least $k$ points of $P$. We present a randomized algorithm that computes in $O( n k )$ expected time such a circle, improving over previously known algorithms. Further, we present a linear time $\delta$-approximation algorithm that outputs a circle that contains at least $k$ points of $P$ and has radius less than $(1+\delta)r_{opt}(P,k)$, where $r_{opt}(P,k)$ is the radius of the minimum circle containing at least $k$ points of $P$. The expected running time of this approximation algorithm is $O(n + n \cdot\min((1/k\delta^3) \log^2 (1/\delta),k))$.