# Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model

@article{Keikha2021ClusteringGP, title={Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model}, author={Vahideh Keikha and Sepideh Aghamolaei and Ali Mohades and Mohammad Ghodsi}, journal={Fundam. Informaticae}, year={2021}, volume={184}, pages={205-231} }

The k-center problem is to choose a subset of size k from a set of n points such that the maximum distance from each point to its nearest center is minimized. Let Q = {Q1, . . . , Qn} be a set of polygons or segments in the region-based uncertainty model, in which each Qi is an uncertain point, where the exact locations of the points in Qi are unknown. The geometric objects such as segments and polygons can be models of a point set. We define the uncertain version of the k-center problem as a…

## One Citation

### Minimum color spanning circle of imprecise points

- Computer Science, MathematicsTheor. Comput. Sci.
- 2022

## References

SHOWING 1-10 OF 48 REFERENCES

### On the Most Likely Convex Hull of Uncertain Points

- Mathematics, Computer ScienceESA
- 2013

The most likely hull under the point model can be computed in O(n 3) time for n points in d = 2 dimensions, but it is NP–hard for d ≥ 3 dimensions, and it is shown that the problem is NP-hard under the multipoint model even for d =2 dimensions.

### Stochastic k-Center and j-Flat-Center Problems

- MathematicsSODA
- 2017

This paper studies two important geometric optimization problems, the k- center problem and the j-flat-center problem, over stochastic/uncertain data points in Euclidean spaces, and provides the first PTAS (Polynomial Time Approximation Scheme) for both problems under the two models.

### Solving k-center Clustering (with Outliers) in MapReduce and Streaming, almost as Accurately as Sequentially

- Computer ScienceProc. VLDB Endow.
- 2019

This paper presents coreset-based 2-round MapReduce algorithms for center-based clustering, and shows that the algorithms become very space-efficient for the important case of small (constant) D .

### Range-Max Queries on Uncertain Data

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 2018

Algorithms for building an index on P so that for a d-dimensional query rectangle ρ, the expected maximum value or the most-likely maximum value in ρ can be computed quickly and extensions to more general uncertainty models and for computing the top-k values of the range-max are presented.

### Optimal algorithms for approximate clustering

- Computer ScienceSTOC '88
- 1988

This work gives a polynomial time approximation scheme that estimates the optimal number of clusters under the second measure of cluster size within factors arbitrarily close to 1 for a fixed cluster size.

### An approximation algorithm for k-center problem on a convex polygon

- Computer ScienceJ. Comb. Optim.
- 2014

An 1.8841-approximation polynomial time algorithm is presented for the constrained version of the k-center location problem, where every point in that region receives service from its closest facility and the maximum service distance is minimized.

### Approximation Algorithms for k-Line Center

- MathematicsESA
- 2002

An algorithm is described that, given P and an ? > 0, computes k cylinders of radius at most (1 + ?)w* that cover P that uses a well-known scheme based on sampling and iterated re-weighting for computing the cylinders.

### Approximation algorithms for clustering uncertain data

- Computer SciencePODS
- 2008

The core mining problem of clustering on uncertain data is studied, and appropriate natural generalizations of standard clustering optimization criteria are defined, and a variety of bicriteria approximation algorithms are shown, including the first known guaranteed approximation algorithms for the problems of clustered uncertain data.

### Largest and Smallest Convex Hulls for Imprecise Points

- Mathematics, Computer ScienceAlgorithmica
- 2008

The problem of computing the smallest and largest possible convex hulls, measured by length and by area, is studied, and polynomial time algorithms for several variants of this problem are given, ranging in running time from O(nlog n) to O( n13).