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Documents authored by Feldkord, Björn

Document
DOI: 10.4230/LIPIcs.STACS.2021.14
A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location

Authors: Marcin Bienkowski, Björn Feldkord, and Paweł Schmidt

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
In the online non-metric variant of the facility location problem, there is a given graph consisting of a set F of facilities (each with a certain opening cost), a set C of potential clients, and weighted connections between them. The online part of the input is a sequence of clients from C, and in response to any requested client, an online algorithm may open an additional subset of facilities and must connect the given client to an open facility. We give an online, polynomial-time deterministic algorithm for this problem, with a competitive ratio of O(log |F| ⋅ (log |C| + log log |F|)). The result is optimal up to loglog factors. Our algorithm improves over the O((log |C| + log |F|) ⋅ (log |C| + log log |F|))-competitive construction that first reduces the facility location instance to a set cover one and then later solves such instance using the deterministic algorithm by Alon et al. [TALG 2006]. This is an asymptotic improvement in a typical scenario where |F| ≪ |C|. We achieve this by a more direct approach: we design an algorithm for a fractional relaxation of the non-metric facility location problem with clustered facilities. To handle the constraints of such non-covering LP, we combine the dual fitting and multiplicative weight updates approach. By maintaining certain additional monotonicity properties of the created fractional solution, we can handle the dependencies between facilities and connections in a rounding routine. Our result, combined with the algorithm by Naor et al. [FOCS 2011] yields the first deterministic algorithm for the online node-weighted Steiner tree problem. The resulting competitive ratio is O(log k ⋅ log² 𝓁) on graphs of 𝓁 nodes and k terminals.
Cite as

Marcin Bienkowski, Björn Feldkord, and Paweł Schmidt. A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bienkowski_et_al:LIPIcs.STACS.2021.14,
  author =	{Bienkowski, Marcin and Feldkord, Bj\"{o}rn and Schmidt, Pawe{\l}},
  title =	{{A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.14},
  URN =		{urn:nbn:de:0030-drops-136598},
  doi =		{10.4230/LIPIcs.STACS.2021.14},
  annote =	{Keywords: Online algorithms, deterministic rounding, linear programming, facility location, set cover}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.51
Fully-Dynamic Bin Packing with Little Repacking

Authors: Björn Feldkord, Matthias Feldotto, Anupam Gupta, Guru Guruganesh, Amit Kumar, Sören Riechers, and David Wajc

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We study the classic bin packing problem in a fully-dynamic setting, where new items can arrive and old items may depart. We want algorithms with low asymptotic competitive ratio while repacking items sparingly between updates. Formally, each item i has a movement cost c_i >= 0, and we want to use alpha * OPT bins and incur a movement cost gamma * c_i, either in the worst case, or in an amortized sense, for alpha, gamma as small as possible. We call gamma the recourse of the algorithm. This is motivated by cloud storage applications, where fully-dynamic bin packing models the problem of data backup to minimize the number of disks used, as well as communication incurred in moving file backups between disks. Since the set of files changes over time, we could recompute a solution periodically from scratch, but this would give a high number of disk rewrites, incurring a high energy cost and possible wear and tear of the disks. In this work, we present optimal tradeoffs between number of bins used and number of items repacked, as well as natural extensions of the latter measure.
Cite as

Björn Feldkord, Matthias Feldotto, Anupam Gupta, Guru Guruganesh, Amit Kumar, Sören Riechers, and David Wajc. Fully-Dynamic Bin Packing with Little Repacking. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 51:1-51:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{feldkord_et_al:LIPIcs.ICALP.2018.51,
  author =	{Feldkord, Bj\"{o}rn and Feldotto, Matthias and Gupta, Anupam and Guruganesh, Guru and Kumar, Amit and Riechers, S\"{o}ren and Wajc, David},
  title =	{{Fully-Dynamic Bin Packing with Little Repacking}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{51:1--51:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.51},
  URN =		{urn:nbn:de:0030-drops-90556},
  doi =		{10.4230/LIPIcs.ICALP.2018.51},
  annote =	{Keywords: Bin Packing, Fully Dynamic, Recourse, Tradeoffs}
}
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