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Documents authored by Byrka, Jaroslaw

Document
DOI: 10.4230/LIPIcs.ICALP.2018.26
Proportional Approval Voting, Harmonic k-median, and Negative Association

Authors: Jaroslaw Byrka, Piotr Skowron, and Krzysztof Sornat

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

Abstract
We study a generic framework that provides a unified view on two important classes of problems: (i) extensions of the k-median problem where clients are interested in having multiple facilities in their vicinity (e.g., due to the fact that, with some small probability, the closest facility might be malfunctioning and so might not be available for using), and (ii) finding winners according to some appealing multiwinner election rules, i.e., election system aimed for choosing representatives bodies, such as parliaments, based on preferences of a population of voters over individual candidates. Each problem in our framework is associated with a vector of weights: we show that the approximability of the problem depends on structural properties of these vectors. We specifically focus on the harmonic sequence of weights, since it results in particularly appealing properties of the considered problem. In particular, the objective function interpreted in a multiwinner election setup reflects to the well-known Proportional Approval Voting (PAV) rule. Our main result is that, due to the specific (harmonic) structure of weights, the problem allows constant factor approximation. This is surprising since the problem can be interpreted as a variant of the k-median problem where we do not assume that the connection costs satisfy the triangle inequality. To the best of our knowledge this is the first constant factor approximation algorithm for a variant of k-median that does not require this assumption. The algorithm we propose is based on dependent rounding [Srinivasan, FOCS'01] applied to the solution of a natural LP-relaxation of the problem. The rounding process is well known to produce distributions over integral solutions satisfying Negative Correlation (NC), which is usually sufficient for the analysis of approximation guarantees offered by rounding procedures. In our analysis, however, we need to use the fact that the carefully implemented rounding process satisfies a stronger property, called Negative Association (NA), which allows us to apply standard concentration bounds for conditional random variables.
Cite as

Jaroslaw Byrka, Piotr Skowron, and Krzysztof Sornat. Proportional Approval Voting, Harmonic k-median, and Negative Association. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{byrka_et_al:LIPIcs.ICALP.2018.26,
  author =	{Byrka, Jaroslaw and Skowron, Piotr and Sornat, Krzysztof},
  title =	{{Proportional Approval Voting, Harmonic k-median, and Negative Association}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{26:1--26:14},
  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.2018.26},
  URN =		{urn:nbn:de:0030-drops-90307},
  doi =		{10.4230/LIPIcs.ICALP.2018.26},
  annote =	{Keywords: approximation algorithms, computational social choice, k-median, dependent rounding, negative association}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.13
Dynamic Beats Fixed: On Phase-Based Algorithms for File Migration

Authors: Marcin Bienkowski, Jaroslaw Byrka, and Marcin Mucha

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
In this paper, we construct a deterministic 4-competitive algorithm for the online file migration problem, beating the currently best 20-year old, 4.086-competitive MTLM algorithm by Bartal et al. (SODA 1997). Like MTLM, our algorithm also operates in phases, but it adapts their lengths dynamically depending on the geometry of requests seen so far. The improvement was obtained by carefully analyzing a linear model (factor-revealing LP) of a single phase of the algorithm. We also show that if an online algorithm operates in phases of fixed length and the adversary is able to modify the graph between phases, no algorithm can beat the competitive ratio of 4.086.
Cite as

Marcin Bienkowski, Jaroslaw Byrka, and Marcin Mucha. Dynamic Beats Fixed: On Phase-Based Algorithms for File Migration. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bienkowski_et_al:LIPIcs.ICALP.2017.13,
  author =	{Bienkowski, Marcin and Byrka, Jaroslaw and Mucha, Marcin},
  title =	{{Dynamic Beats Fixed: On Phase-Based Algorithms for File Migration}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.13},
  URN =		{urn:nbn:de:0030-drops-73942},
  doi =		{10.4230/LIPIcs.ICALP.2017.13},
  annote =	{Keywords: file migration, factor-revealing linear programs, online algorithms, competitive analysis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.12
Online Algorithms for Multi-Level Aggregation

Authors: Marcin Bienkowski, Martin Böhm, Jaroslaw Byrka, Marek Chrobak, Christoph Dürr, Lukas Folwarczny, Lukasz Jez, Jiri Sgall, Nguyen Kim Thang, and Pavel Vesely

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the TCP Acknowledgment Problem, while for trees of depth 2, it is equivalent to the Joint Replenishment Problem. Aggregation problem for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and in supply-chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant competitive online algorithm for networks of arbitrary (fixed) number of levels. The competitive ratio is O(D^4*2^D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines. We include several additional results in the paper. We show that a standard lower-bound technique for MLAP, based on so-called Single-Phase instances, cannot give super-constant lower bounds (as a function of the tree depth). This result is established by giving an online algorithm with optimal competitive ratio 4 for such instances on arbitrary trees. We also study the MLAP variant when the tree is a path, for which we give a lower bound of 4 on the competitive ratio, improving the lower bound known for general MLAP. We complement this with a matching upper bound for the deadline setting.
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Marcin Bienkowski, Martin Böhm, Jaroslaw Byrka, Marek Chrobak, Christoph Dürr, Lukas Folwarczny, Lukasz Jez, Jiri Sgall, Nguyen Kim Thang, and Pavel Vesely. Online Algorithms for Multi-Level Aggregation. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bienkowski_et_al:LIPIcs.ESA.2016.12,
  author =	{Bienkowski, Marcin and B\"{o}hm, Martin and Byrka, Jaroslaw and Chrobak, Marek and D\"{u}rr, Christoph and Folwarczny, Lukas and Jez, Lukasz and Sgall, Jiri and Kim Thang, Nguyen and Vesely, Pavel},
  title =	{{Online Algorithms for Multi-Level Aggregation}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.12},
  URN =		{urn:nbn:de:0030-drops-63637},
  doi =		{10.4230/LIPIcs.ESA.2016.12},
  annote =	{Keywords: algorithmic aspects of networks, online algorithms, scheduling and resource allocation}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2016.2
Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs

Authors: Jaroslaw Byrka, Mateusz Lewandowski, and Carsten Moldenhauer

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
We study the prize-collecting version of the node-weighted Steiner tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show a 2.88-approximation which establishes a new best approximation guarantee for planar NWPCST. This is done by combining our LMP algorithm with a threshold rounding technique and utilizing the 2.4-approximation of Berman and Yaroslavtsev [6] for the version without penalties. We also give a primal-dual 4-approximation algorithm for the more general forest version using techniques introduced by Hajiaghay and Jain [17].
Cite as

Jaroslaw Byrka, Mateusz Lewandowski, and Carsten Moldenhauer. Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{byrka_et_al:LIPIcs.SWAT.2016.2,
  author =	{Byrka, Jaroslaw and Lewandowski, Mateusz and Moldenhauer, Carsten},
  title =	{{Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.2},
  URN =		{urn:nbn:de:0030-drops-60313},
  doi =		{10.4230/LIPIcs.SWAT.2016.2},
  annote =	{Keywords: approximation algorithms, Node-Weighted Steiner Tree, primal-dual algorithm, LMP, planar graphs}
}
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