3 research outputs found
Improvements on the k-center problem for uncertain data
In real applications, there are situations where we need to model some
problems based on uncertain data. This leads us to define an uncertain model
for some classical geometric optimization problems and propose algorithms to
solve them. In this paper, we study the -center problem, for uncertain
input. In our setting, each uncertain point is located independently from
other points in one of several possible locations in a metric space with metric , with specified probabilities
and the goal is to compute -centers that minimize the
following expected cost here
is the probability space of all realizations of given uncertain points and
In restricted assigned version of this problem, an assignment is given for any choice of centers and the
goal is to minimize In unrestricted version, the
assignment is not specified and the goal is to compute centers
and an assignment that minimize the above expected
cost.
We give several improved constant approximation factor algorithms for the
assigned versions of this problem in a Euclidean space and in a general metric
space. Our results significantly improve the results of \cite{guh} and
generalize the results of \cite{wang} to any dimension. Our approach is to
replace a certain center point for each uncertain point and study the
properties of these certain points. The proposed algorithms are efficient and
simple to implement
Diverse sampling of streaming data
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 49-51).This thesis addresses the problem of diverse sampling as a dispersion problem and proposes solutions that are optimized for large streaming data. Finding the optimal solution to the dispersion problem is NP-hard. Therefore, existing and proposed solutions are approximation algorithms. This work evaluates the performance of dierent algorithms in practice and compares them to the theoretical guarantees.by Aizana Turmukhametova.M. Eng