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Approximation algorithms for geometric median problems
1992
Information Processing Letters
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In this paper we present approximation algorithms for median problems in metric spaces and xed-dimensional Euclidean space. ...
Our algorithms use a new method for transforming an optimal solution of the linear program relaxation of the s-median problem into a provably good integral solution. ...
For approximation algorithms for the s-center problem, we refer the readers to FeG,Gon, HoS ...
doi:10.1016/0020-0190(92)90208-d
fatcat:63iziixt4ndjpjrbaati3ps6mi
Approximation schemes for Euclidean k-medians and related problems
1998
Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98
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The approximation scheme also generalizes to some problems related to k-median. ...
Our methodology is to extend Arora's [1, 2] techniques for the TSP, which hitherto seemed inapplicable to problems such as the k-median problem. ...
algorithms for other geometric problems. ...
doi:10.1145/276698.276718
dblp:conf/stoc/AroraRR98
fatcat:our5vrenlndahmpnie7rqb2nti
A Multi-Objective Optimization Algorithm for Center-Based Clustering
2020
Electronical Notes in Theoretical Computer Science
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Also, an approximation algorithm for the discrete k -center problem is used as a local search strategy for initializing the population. ...
Also, an approximation algorithm for the k -center problem is used as local search for generating initial solutions, that is, initial places for starting the search. ...
The approximation problem has been widely studied for a great number of points, giving as result many polinomial time algorithms for the approximate geometric median problem. ...
doi:10.1016/j.entcs.2020.02.012
fatcat:zqllwpxzbbbmjgxitm23q5ghdq
Subject Index
2007
Journal of Discrete Algorithms
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polygon, 524
Sorting algorithm
Asymptotic distributions for Random Median Quicksort, 592
Sorting buffers
Exploiting locality: approximating sorting buffers, 729
Stable matching problem
Two algorithms ...
Character sets of strings, 330; A linear time algorithm for the inver-Label Cover Approximation algorithms for the Label-Cover MAX and Red-Blue Set Cover problems, 55 Lattice animals On the complexity ...
doi:10.1016/s1570-8667(07)00076-7
fatcat:wfqxglrznfb6do3wyittd5pfbi
Proportional Approval Voting, Harmonic k-median, and Negative Association
2018
International Colloquium on Automata, Languages and Programming
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To the best of our knowledge this is the first constant factor approximation algorithm for a variant of k-median that does not require this assumption. ...
ACM Subject Classification Theory of computation → Approximation algorithms analysis ...
Indeed, the (2.675 + )-approximation algorithm for k-median [5] , the 93-approximation algorithm for Fault Tolerant k-median [17] , the 2-approximation algorithm for k-center [18] , and the 6.357-approximation ...
doi:10.4230/lipics.icalp.2018.26
dblp:conf/icalp/ByrkaSS18
fatcat:ij4ywi47pjf6togjdvlng4b7wu
Weber's problem on the Riemannian Manifolds: Some upper bounds for the minimun Weber's function
El problema de Weber sobre variedades Riemannianas: Algunas cotas Superiores para el mínimo de la función de Weber
2019
Selecciones Matemáticas
El problema de Weber sobre variedades Riemannianas: Algunas cotas Superiores para el mínimo de la función de Weber
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Keywords: The Weber problem, Weighted Geometric Median, Riemannian manifold, Strongly convex set. ...
weighted geometric median of "m" given points in the strongly convex. ...
Case
Figure 3 . 3 The red point is the geometric median for 20 points.
Table 2. ...
doi:10.17268/sel.mat.2019.01.13
fatcat:4fqdkhzq45dsbiozq3ogp5av7a
Algorithms for dynamic geometric problems over data streams
2004
Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04
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Acknowledgments: The author would like to thank Graham Cormode, Sudipto Guha and Muthu Muthukrishnan, for helpful discussions. ...
This gives us a bicriterion [O(log ∆), 1 + ]-approximate algorithm for the k-median problem. The time to construct the medians is still Ω(∆ 2 ). ...
We provide a novel algorithm for this problem. Finally, the quantity needed for the k-median problem can be computed using a variant of an algorithm for the heavy-hitters problem as in [9] . ...
doi:10.1145/1007352.1007413
dblp:conf/stoc/Indyk04
fatcat:nky6vxbnkneutjopnprhlqhcgy
SOMICA and geometric ICA
2003
Sixth International Conference of Information Fusion, 2003. Proceedings of the
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In this paper we use this fact and present a new geometric ICA algorithm that uses a SOM for learning. ...
The separation qualiry is better in comparison to other geometric algorithms, but the computational cost is highe,: Furthermore. this new algorithm will pmvide insight in how to transfer theoretical results ...
Conclusion We presented a new algorithm for linear ICA similar to geometric ICA using a SOM for the mixture space approximation. ...
doi:10.1109/icif.2003.177411
fatcat:yzmsit2jsvcydmyvuktnkyphne
The Flag Median and FlagIRLS
[article]
2022
arXiv
pre-print
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., mean and median) for a dataset is central to a number of common machine learning algorithms. ...
The flag median is compared the other leading algorithms for computing prototypes on the Grassmannian, namely, the ℓ_2-median and to the flag mean. ...
An iterative algorithm for approximating a geometric median is the Weiszfeld algorithm [1] ; each iteration of this algorithm is a weighted centroid problem. ...
arXiv:2203.04437v1
fatcat:egh4aamt3banvmr2efbf6e7br4
Deterministic sampling and range counting in geometric data streams
2007
ACM Transactions on Algorithms
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We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. ...
Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries. ...
Muthukrishnan for helpful discussions on geometric streaming algorithms in general. ...
doi:10.1145/1240233.1240239
fatcat:6i5xklofj5c7fdu7ufsjambram
On k-Median clustering in high dimensions
2006
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
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We study approximation algorithms for k-median clustering. We obtain small coresets for k-median clustering in metric spaces as well as in Euclidean spaces. ...
This is the first streaming algorithm, for this problem, that has space complexity with only polynomial dependency on the dimension. ...
Acknowledgments The author thanks Sariel Har-Peled for helpful discussions on the problems studied in the paper and ...
doi:10.1145/1109557.1109687
fatcat:lhh4wcanrfhw5opbwkszym3ycu
Deterministic sampling and range counting in geometric data streams
2004
Proceedings of the twentieth annual symposium on Computational geometry - SCG '04
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We present memory-efficient deterministic algorithms for constructing -nets and -approximations of streams of geometric data. ...
We also include a lower bound for non-iceberg geometric queries. ...
Muthukrishnan for helpful discussions on geometric streaming algorithms in general. ...
doi:10.1145/997817.997842
dblp:conf/compgeom/BagchiCEG04
fatcat:nhyx7iw4vjelhgbxtmftzfbsqu
Clustering on Sliding Windows in Polylogarithmic Space
2015
Foundations of Software Technology and Theoretical Computer Science
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In PODS 2003, Babcock, Datar, Motwani and O'Callaghan [4] gave the first streaming solution for the k-median problem on sliding windows using O( k τ 4 W 2τ log 2 W) space, with a O(2 O(1/τ) ) approximation ...
In particular, we give the first polylogarithmic space (α, β)approximation for metric k-median clustering in the sliding window model, where α and β are constants, under the assumption, also made by Babcock ...
We say an algorithm A is an (α, β)-approximation algorithm for the k-median problem on a point set P ⊂ X if A(P, k) returns a set C ⊂ P of at most β · k centers whose cost is α-approximation of OPT(P, ...
doi:10.4230/lipics.fsttcs.2015.350
dblp:conf/fsttcs/BravermanLLM15
fatcat:2tly3cxflfdgxltbthhmka234y
Byzantine-Robust Federated Linear Bandits
[article]
2022
arXiv
pre-print
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We propose a novel algorithm with a robust aggregation oracle that utilizes the geometric median. ...
Finally, if the level of corruption is known to be small, we show that using the geometric median of mean oracle for robust aggregation further improves the regret bound. ...
Of all these methods, we focus on geometric median and geometric median of mean for aggregation. Also, ǫ-approximation of the two values are considered for tractability [Pillutla et al., 2019] . ...
arXiv:2204.01155v1
fatcat:64deqod4xfcmnbj34jtybxvzpa
MAC Advice for Facility Location Mechanism Design
[article]
2024
arXiv
pre-print
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We show that the 1-median (geometric median) of a set of points is naturally robust under corruptions, which leads to an algorithm for single-facility location with MAC predictions. ...
However, these predictions are only "mostly" and "approximately" correct (or MAC for short) – i.e., some δ-fraction of the predicted locations are allowed to be arbitrarily incorrect, and the remainder ...
Acknowledgements We are grateful to Batya Berzack for comments on an earlier draft of the paper. ...
arXiv:2403.12181v1
fatcat:dp5f5ljnejgs7ehdi6iwunz5uy
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