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Better bounds for incremental medians

Marek Chrobak, Mathilde Hurand
2011 Theoretical Computer Science  
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]

Marek Chrobak, Mathilde Hurand
Approximation and Online Algorithms  
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

Chandrashekhar Nagarajan, David P. Williamson
2013 ACM Journal of Experimental Algorithmics  
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]

Chandrashekhar Nagarajan, David P. Williamson
2011 Lecture Notes in Computer Science  
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

Marek Chrobak, Claire Kenyon, John Noga, Neal E. Young
2007 Algorithmica  
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

R A Whitaker
1981 Environment and planning A  
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

Christos Kaklamanis, Martin Skutella
2011 Theoretical Computer Science  
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

Marek Chrobak, Claire Kenyon, Neal Young
2006 Information Processing Letters  
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]

Marek Chrobak, Claire Kenyon, Neal E. Young
2005 Lecture Notes in Computer Science  
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

Approximation algorithms for hierarchical location problems

C. Greg Plaxton
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 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

Fast median search in metric spaces [chapter]

A. Juan, E. Vidal
1998 Lecture Notes in Computer Science  
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

C. Greg Plaxton
2006 Journal of computer and system sciences (Print)  
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

C. Greg Plaxton
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 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]

Ethan Burns, Wheeler Ruml
2012 Lecture Notes in Computer Science  
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

SIGACT news online algorithms column 2

Marek Chrobak
2004 ACM SIGACT News  
The term "doubling" is a little misleading, 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  ... 
doi:10.1145/970831.970841 fatcat:aouhalb5yvacjdspnm4hpucifu
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