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Better bounds for incremental medians
2011
Theoretical Computer Science
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Williamson, A general approach for incremental approximation and hierarchical clustering, in: We improve both bounds in this paper. ...
In the incremental version of the well-known k-median problem, the objective is to compute an incremental sequence of facility sets F 1 ⊆ F 2 ⊆ · · · ⊆ F n , where each F k contains at most k facilities ...
Acknowledgments We would like to thank the anonymous referees for useful comments and for pointing out several mistakes in the earlier draft of this paper. ...
doi:10.1016/j.tcs.2009.07.006
fatcat:exhgsfotgnhx3owvmo6opk3coy
Better Bounds for Incremental Medians
[chapter]
Approximation and Online Algorithms
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Williamson, A general approach for incremental approximation and hierarchical clustering, in: We improve both bounds in this paper. ...
In the incremental version of the well-known k-median problem, the objective is to compute an incremental sequence of facility sets F 1 ⊆ F 2 ⊆ · · · ⊆ F n , where each F k contains at most k facilities ...
Acknowledgments We would like to thank the anonymous referees for useful comments and for pointing out several mistakes in the earlier draft of this paper. ...
doi:10.1007/978-3-540-77918-6_17
dblp:conf/waoa/ChrobakH07
fatcat:thgazgbyljbezel3cwhintvhvu
An Experimental Evaluation of Incremental and Hierarchicalk-Median Algorithms
2013
ACM Journal of Experimental Algorithmics
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The optimal solution can be fractional but still gives a good lower bound for the k-median problem. ...
Mettu and Plaxton [10] gave a 29.86-competitive algorithm for the incremental k-median problem. ...
The bounded envelope gives 2-approximate solutions for the k-median problem for some values of k as well as a corresponding piecewise linear lower bound on the values of k-median solutions for all values ...
doi:10.1145/2543628
fatcat:m5ddg7yclbhzhhbektyjo27jc4
An Experimental Evaluation of Incremental and Hierarchical k-Median Algorithms
[chapter]
2011
Lecture Notes in Computer Science
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The optimal solution can be fractional but still gives a good lower bound for the k-median problem. ...
Mettu and Plaxton [10] gave a 29.86-competitive algorithm for the incremental k-median problem. ...
The bounded envelope gives 2-approximate solutions for the k-median problem for some values of k as well as a corresponding piecewise linear lower bound on the values of k-median solutions for all values ...
doi:10.1007/978-3-642-20662-7_15
fatcat:cb5znuhogfc53awmuhgelcikfi
Incremental Medians via Online Bidding
2007
Algorithmica
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Following Mettu and Plaxton, we study online algorithms for the k-medians problem. Such an algorithm must produce a nested sequence F_1\subseteq F_2\subseteq...\subseteq F_n of sets of facilities. ...
We present optimally competitive algorithms for this problem. ...
Acknowledgements We are grateful to anonymous referees for suggestions to improve the presentation. ...
doi:10.1007/s00453-007-9005-x
fatcat:pijjbiqwdjhwrmtsxseibrkqli
A Tight Bound Drop Exchange Algorithm for Solving the p Median Problem
1981
Environment and planning A
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In solving for a fixed value of p, tight bounds on all other median solutions in the range m-\ to p4-1 are generated where m is the number of possible location sites and p is the number of medians. ...
A drop algorithm is proposed for solving the p median problem. ...
The author gratefully acknowledges the Department of Geography, University of British Columbia, for providing computer resources, and in particular Mike Church whose support and encouragement made possible ...
doi:10.1068/a130669
fatcat:pe53duzyxze4dnrwdrdmtgmxqu
Preface
2011
Theoretical Computer Science
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While, for the case k = 2, this problem is well-understood with respect to * Corresponding editor. ...
Of 56 papers submitted to WAOA 2007, there were 22 accepted for presentation at the workshop, and revised versions of 7 papers appear in this special issue. ...
In their article Better bounds for incremental medians, Marek Chrobak and Mathilde Hurand present improved upper and lower bounds on the competitive ratio of incremental median sequences. ...
doi:10.1016/j.tcs.2010.12.050
fatcat:lyktg43elrdyho3uj6xgjm4rei
The reverse greedy algorithm for the metric k-median problem
2006
Information Processing Letters
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The Reverse Greedy algorithm (RGreedy) for the k-median problem works as follows. It starts by placing facilities on all nodes. ...
Acknowledgements We would like to thank Amos Fiat, Christoph Dürr, Jason Hartline, Anna Karlin, and John Noga for useful discussions. ...
This problem is called online median in [9] , incremental median in [10] , and the analog version for clustering is called oblivious clustering in [2, 3] . ...
doi:10.1016/j.ipl.2005.09.009
fatcat:2hgqeqd7pzdjzcl2yi3k7bae7q
The Reverse Greedy Algorithm for the Metric K-Median Problem
[chapter]
2005
Lecture Notes in Computer Science
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The Reverse Greedy algorithm (RGREEDY) for the k-median problem works as follows. It starts by placing facilities on all nodes. ...
Acknowledgements We would like to thank Amos Fiat, Christoph Dürr, Jason Hartline, Anna Karlin, and John Noga for useful discussions. ...
This problem is called online median in [9] , incremental median in [10] , and the analog version for clustering is called oblivious clustering in [2, 3] . ...
doi:10.1007/11533719_66
fatcat:u2yf7hvx4fhe3a33qqut6oqh3a
Fast median search in metric spaces
[chapter]
1998
Lecture Notes in Computer Science
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Searching for a median of a set of patterns is a well-known technique to model the set or to aid searching for more accurate models such as a generalized median or a k-median. ...
In these cases, a direct method to perform median search is not feasible for large sets of patterns. ...
In these cases where such computation is not trivial, a median can be used as an approximate generalized median or as a starting point for finding better ones [5] . ...
doi:10.1007/bfb0033318
fatcat:4k7jqgtrinhzpdu7ux6ber55zy
Approximation algorithms for hierarchical location problems
2003
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
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A key building block of our hierarchical facility location algorithm is a constantfactor approximation algorithm for an "incremental" variant of the facility location problem; the latter algorithm may ...
We formulate and (approximately) solve hierarchical versions of two prototypical problems in discrete location theory, namely, the metric uncapacitated k-median and facility location problems. ...
Acknowledgments The author would like to thank Sanjoy Dasgupta, Samir Khuller, Xiaozhou Li, Ramgopal Mettu, Vinayaka Pandit, Yu Sun, and Arun Venkataramani for their ...
doi:10.1145/780542.780549
dblp:conf/stoc/Plaxton03
fatcat:y3rvflbzaravvljdkjwa6jy3ji
Approximation algorithms for hierarchical location problems
2006
Journal of computer and system sciences (Print)
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A key building block of our hierarchical facility location algorithm is a constantfactor approximation algorithm for an "incremental" variant of the facility location problem; the latter algorithm may ...
We formulate and (approximately) solve hierarchical versions of two prototypical problems in discrete location theory, namely, the metric uncapacitated k-median and facility location problems. ...
Acknowledgments The author would like to thank Sanjoy Dasgupta, Samir Khuller, Xiaozhou Li, Ramgopal Mettu, Vinayaka Pandit, Yu Sun, and Arun Venkataramani for their ...
doi:10.1016/j.jcss.2005.09.004
fatcat:akkavx2lzfgwres6thubqwdz6a
Approximation algorithms for hierarchical location problems
2003
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
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A key building block of our hierarchical facility location algorithm is a constantfactor approximation algorithm for an "incremental" variant of the facility location problem; the latter algorithm may ...
We formulate and (approximately) solve hierarchical versions of two prototypical problems in discrete location theory, namely, the metric uncapacitated k-median and facility location problems. ...
Acknowledgments The author would like to thank Sanjoy Dasgupta, Samir Khuller, Xiaozhou Li, Ramgopal Mettu, Vinayaka Pandit, Yu Sun, and Arun Venkataramani for their ...
doi:10.1145/780547.780549
fatcat:itw45wpcsjfujaijpxl5zv7h5a
Iterative-Deepening Search with On-Line Tree Size Prediction
[chapter]
2012
Lecture Notes in Computer Science
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The best-known approach for coping with this issue is iterative deepening, which performs a series of bounded depth-first searches. ...
While it happens to work acceptably for the classic sliding tile puzzle, IDA* fails for many other domains. ...
The median estimation factor for the incremental model was 1.435 and the median estimation factor for CDP was 1.465 on this set of instances. ...
doi:10.1007/978-3-642-34413-8_1
fatcat:2ieiirvywvc3zct2zirgem4cli
Incremental Division of Very Large Point Clouds for Scalable 3D Surface Reconstruction
2015
2015 IEEE International Conference on Computer Vision Workshop (ICCVW)
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In this paper we, therefore, present an algorithm for division of very large 3D point clouds into smaller subsets allowing for a parallel 3D reconstruction of many suitably small parts. ...
Space division is especially important for volumetric 3D reconstruction, as the latter has a high memory requirement. ...
While the calculation of a dominant space dimension is feasible also when taking into account our scalability constraint via bounding boxes, the calculation of the median does not scale well. ...
doi:10.1109/iccvw.2015.30
dblp:conf/iccvw/KuhnM15
fatcat:zy5wdo6o5jfqnitd6iwcdjq4sa
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