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k-center-problem
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Massively Parallel Clustering with Outliers
, M.Sc. Thesis Sharif University of Technology ; Zarrabizadeh, Hamid (Supervisor)
Abstract
Clustering is a fundamental problem for data analysis, and it has a lot of variants. In this thesis we focused on the k-center problem, which is one of the most popular and well-studied variants of clustering. In this problem we are given a metric set of points called X, and a parameter k ⩽ |X|. Our goal is to find a set of k centers in X, minimizing the maximum distance of any point of X from its closest center. This thesis has worked on a version of the problem that is harder to solve. we have an extra parameter called z, which represents the maximum number of points that there is no need to be clustered, and we refer to them as outliers. The growth of data that needs to be processed makes...
Preclustering algorithms for imprecise points
, Article 17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020, 22 June 2020 through 24 June 2020 ; Volume 162 , 2020 ; de Berg, M ; Farahzad, S ; Haji Mirsadeghi, M. O ; Saghafian, M ; Sharif University of Technology
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
2020
Abstract
We study the problem of preclustering a set B of imprecise points in Rd: we wish to cluster the regions specifying the potential locations of the points such that, no matter where the points are located within their regions, the resulting clustering approximates the optimal clustering for those locations. We consider k-center, k-median, and k-means clustering, and obtain the following results. Let B := {b1, . . ., bn} be a collection of disjoint balls in Rd, where each ball bi specifies the possible locations of an input point pi. A partition C of B into subsets is called an (f(k), α)preclustering (with respect to the specific k-clustering variant under consideration) if (i) C consists of...
Improved algorithms for distributed balanced clustering
, Article 3rd IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science, TTCS 2020, 1 July 2020 through 2 July 2020 ; Volume 12281 LNCS , 2020 , Pages 72-84 ; Zarrabizadeh, H ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2020
Abstract
We study a weighted balanced version of the k-center problem, where each center has a fixed capacity, and each element has an arbitrary demand. The objective is to assign demands of the elements to the centers, so as the total demand assigned to each center does not exceed its capacity, while the maximum distance between centers and their assigned elements is minimized. We present a deterministic O(1)-approximation algorithm for this generalized version of the k-center problem in the distributed setting, where data is partitioned among a number of machines. Our algorithm substantially improves the approximation factor of the current best randomized algorithm available for the problem. We...
Preclustering algorithms for imprecise points
, Article Algorithmica ; Volume 84, Issue 6 , 2022 , Pages 1467-1489 ; 01784617 (ISSN) ; de Berg, M ; Farahzad, S ; Haji Mirsadeghi, M. O ; Saghafian, M ; Sharif University of Technology
Springer
2022
Abstract
We study the problem of preclustering a set B of imprecise points in Rd: we wish to cluster the regions specifying the potential locations of the points such that, no matter where the points are located within their regions, the resulting clustering approximates the optimal clustering for those locations. We consider k-center, k-median, and k-means clustering, and obtain the following results. Let B: = { b1, … , bn} be a collection of disjoint balls in Rd, where each ball bi specifies the possible locations of an input point pi. A partition C of B into subsets is called an (f(k) , α) -preclustering (with respect to the specific k-clustering variant under consideration) if (i) C consists of...