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Better bounds for incremental medians

2011
*
Theoretical Computer Science
*

Williamson, A general approach

doi:10.1016/j.tcs.2009.07.006
fatcat:exhgsfotgnhx3owvmo6opk3coy
*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. ...##
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Better Bounds for Incremental Medians
[chapter]

*
Approximation and Online Algorithms
*

Williamson, A general approach

doi:10.1007/978-3-540-77918-6_17
dblp:conf/waoa/ChrobakH07
fatcat:thgazgbyljbezel3cwhintvhvu
*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. ...##
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An Experimental Evaluation of Incremental and Hierarchicalk-Median Algorithms

2013
*
ACM Journal of Experimental Algorithmics
*

The optimal solution can be fractional but still gives a good lower

doi:10.1145/2543628
fatcat:m5ddg7yclbhzhhbektyjo27jc4
*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 ...##
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An Experimental Evaluation of Incremental and Hierarchical k-Median Algorithms
[chapter]

2011
*
Lecture Notes in Computer Science
*

The optimal solution can be fractional but still gives a good lower

doi:10.1007/978-3-642-20662-7_15
fatcat:cb5znuhogfc53awmuhgelcikfi
*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 ...##
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Incremental Medians via Online Bidding

2007
*
Algorithmica
*

Following Mettu and Plaxton, we study online algorithms

doi:10.1007/s00453-007-9005-x
fatcat:pijjbiqwdjhwrmtsxseibrkqli
*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. ...##
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A Tight Bound Drop Exchange Algorithm for Solving the p Median Problem

1981
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Environment and planning A
*

In solving

doi:10.1068/a130669
fatcat:pe53duzyxze4dnrwdrdmtgmxqu
*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 ...##
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Preface

2011
*
Theoretical Computer Science
*

While,

doi:10.1016/j.tcs.2010.12.050
fatcat:lyktg43elrdyho3uj6xgjm4rei
*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. ...##
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The reverse greedy algorithm for the metric k-median problem

2006
*
Information Processing Letters
*

The Reverse Greedy algorithm (RGreedy)

doi:10.1016/j.ipl.2005.09.009
fatcat:2hgqeqd7pzdjzcl2yi3k7bae7q
*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] . ...##
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The Reverse Greedy Algorithm for the Metric K-Median Problem
[chapter]

2005
*
Lecture Notes in Computer Science
*

The Reverse Greedy algorithm (RGREEDY)

doi:10.1007/11533719_66
fatcat:u2yf7hvx4fhe3a33qqut6oqh3a
*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] . ...##
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Approximation algorithms for hierarchical location problems

2003
*
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
*

A key building block of our hierarchical facility location algorithm is a constantfactor approximation algorithm

doi:10.1145/780542.780549
dblp:conf/stoc/Plaxton03
fatcat:y3rvflbzaravvljdkjwa6jy3ji
*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 ...##
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Fast median search in metric spaces
[chapter]

1998
*
Lecture Notes in Computer Science
*

Searching

doi:10.1007/bfb0033318
fatcat:4k7jqgtrinhzpdu7ux6ber55zy
*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] . ...##
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Approximation algorithms for hierarchical location problems

2006
*
Journal of computer and system sciences (Print)
*

A key building block of our hierarchical facility location algorithm is a constantfactor approximation algorithm

doi:10.1016/j.jcss.2005.09.004
fatcat:akkavx2lzfgwres6thubqwdz6a
*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 ...##
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Approximation algorithms for hierarchical location problems

2003
*
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
*

A key building block of our hierarchical facility location algorithm is a constantfactor approximation algorithm

doi:10.1145/780547.780549
fatcat:itw45wpcsjfujaijpxl5zv7h5a
*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 ...##
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Iterative-Deepening Search with On-Line Tree Size Prediction
[chapter]

2012
*
Lecture Notes in Computer Science
*

The best-known approach

doi:10.1007/978-3-642-34413-8_1
fatcat:2ieiirvywvc3zct2zirgem4cli
*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. ...##
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SIGACT news online algorithms column 2

2004
*
ACM SIGACT News
*

The term "doubling" is a little misleading,

doi:10.1145/970831.970841
fatcat:aouhalb5yvacjdspnm4hpucifu
*for*often factors other than 2 are used, and suggestions*for*a*better*name will be appreciated. ... We can do*better*with randomization, by choosing the bid sequence (d ) at random so that d k /u is, in expectation, less than the worst case d k /d k−1 . ...*Incremental**Medians*Given an integer k and a metric space, we want to find a set F of k points called facilities*for*which the sum of distances between each point and its closest facility in F is minimized ...
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