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Documents authored by Leniowski, Dariusz


Document
A Tree Structure For Dynamic Facility Location

Authors: Gramoz Goranci, Monika Henzinger, and Dariusz Leniowski

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)


Abstract
We study the metric facility location problem with client insertions and deletions. This setting differs from the classic dynamic facility location problem, where the set of clients remains the same, but the metric space can change over time. We show a deterministic algorithm that maintains a constant factor approximation to the optimal solution in worst-case time O~(2^{O(kappa^2)}) per client insertion or deletion in metric spaces while answering queries about the cost in O(1) time, where kappa denotes the doubling dimension of the metric. For metric spaces with bounded doubling dimension, the update time is polylogarithmic in the parameters of the problem.

Cite as

Gramoz Goranci, Monika Henzinger, and Dariusz Leniowski. A Tree Structure For Dynamic Facility Location. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 39:1-39:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{goranci_et_al:LIPIcs.ESA.2018.39,
  author =	{Goranci, Gramoz and Henzinger, Monika and Leniowski, Dariusz},
  title =	{{A Tree Structure For Dynamic Facility Location}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{39:1--39:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.39},
  URN =		{urn:nbn:de:0030-drops-95026},
  doi =		{10.4230/LIPIcs.ESA.2018.39},
  annote =	{Keywords: facility location, dynamic algorithm, approximation, doubling dimension}
}
Document
Dynamic Clustering to Minimize the Sum of Radii

Authors: Monika Henzinger, Dariusz Leniowski, and Claire Mathieu

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)


Abstract
In this paper, we study the problem of opening centers to cluster a set of clients in a metric space so as to minimize the sum of the costs of the centers and of the cluster radii, in a dynamic environment where clients arrive and depart, and the solution must be updated efficiently while remaining competitive with respect to the current optimal solution. We call this dynamic sum-of-radii clustering problem. We present a data structure that maintains a solution whose cost is within a constant factor of the cost of an optimal solution in metric spaces with bounded doubling dimension and whose worst-case update time is logarithmic in the parameters of the problem.

Cite as

Monika Henzinger, Dariusz Leniowski, and Claire Mathieu. Dynamic Clustering to Minimize the Sum of Radii. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 48:1-48:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{henzinger_et_al:LIPIcs.ESA.2017.48,
  author =	{Henzinger, Monika and Leniowski, Dariusz and Mathieu, Claire},
  title =	{{Dynamic Clustering to Minimize the Sum of Radii}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{48:1--48:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.48},
  URN =		{urn:nbn:de:0030-drops-78749},
  doi =		{10.4230/LIPIcs.ESA.2017.48},
  annote =	{Keywords: dynamic algorithm, clustering, approximation, doubling dimension}
}
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