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Quick k-Median, k-Center, and Facility Location for Sparse Graphs

Author:

Mikkel ThorupAuthors Info & Claims

SIAM Journal on Computing, Volume 34, Issue 2

Pages 405 - 432

https://doi.org/10.1137/S0097539701388884

Published: 01 February 2005 Publication History

Abstract

We present $\tilde{O}(m)$ time and space constant factor approximation algorithms for the k-median, k-center, and facility location problems with assignment costs being shortest path distances in a weighted undirected graph with n vertices and m edges. For all of these location problems, $\tilde{O}(n^2)$ time and space algorithms were already known, but here we are addressing large sparse graphs. An application could be placement of content distributing servers on the Internet. The Internet is large and changes so frequently that an $\tilde{O}(n^2)$ time solution would likely be outdated long before completion.

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Xue YChen XLi TJiang SKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Near-optimal quantum coreset construction algorithms for clusteringProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3620028(38881-38912)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3620028
Banerjee S(2022)A survey on mining and analysis of uncertain graphsKnowledge and Information Systems10.1007/s10115-022-01681-w64:7(1653-1689)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s10115-022-01681-w
Braverman VJiang SKrauthgamer RWu XMarx D(2021)Coresets for clustering in excluded-minor graphs and beyondProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458223(2679-2696)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458223
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Index Terms

Quick k-Median, k-Center, and Facility Location for Sparse Graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
  2. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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Published In

SIAM Journal on Computing Volume 34, Issue 2

2005

253 pages

ISSN:0097-5397

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 February 2005

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Xue YChen XLi TJiang SKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Near-optimal quantum coreset construction algorithms for clusteringProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3620028(38881-38912)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3620028
Banerjee S(2022)A survey on mining and analysis of uncertain graphsKnowledge and Information Systems10.1007/s10115-022-01681-w64:7(1653-1689)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s10115-022-01681-w
Braverman VJiang SKrauthgamer RWu XMarx D(2021)Coresets for clustering in excluded-minor graphs and beyondProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458223(2679-2696)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458223
Cohen-Addad VFeldmann ASaulpic D(2021)Near-linear Time Approximation Schemes for Clustering in Doubling MetricsJournal of the ACM10.1145/347754168:6(1-34)Online publication date: 31-Oct-2021
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Bandyapadhyay SInamdar TPai SPemmaraju S(2021)Near-optimal clustering in the k-machine modelTheoretical Computer Science10.1016/j.tcs.2021.11.026899:C(80-97)Online publication date: 30-Dec-2021
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Abboud AWilliams VWang J(2016)Approximation and fixed parameter subquadratic algorithms for radius and diameter in sparse graphsProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884463(377-391)Online publication date: 10-Jan-2016
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Improved Combinatorial Algorithms for the Facility Location and k-Median Problems

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