2 Search Results for "Sornat, Krzysztof"

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-dev.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.MFCS.2016.9
Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results

Authors: Georgios Amanatidis, Evangelos Markakis, and Krzysztof Sornat

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
We study a revenue maximization problem in the context of social networks. Namely, we consider a model introduced by Alon, Mansour, and Tennenholtz (EC 2013) that captures inequity aversion, i.e., prices offered to neighboring vertices should not be significantly different. We first provide approximation algorithms for a natural class of instances, referred to as the class of single-value revenue functions. Our results improve on the current state of the art, especially when the number of distinct prices is small. This applies, for example, to settings where the seller will only consider a fixed number of discount types or special offers. We then resolve one of the open questions posed in Alon et al., by establishing APX-hardness for the problem. Surprisingly, we further show that the problem is NP-complete even when the price differences are allowed to be relatively large. Finally, we also provide some extensions of the model of Alon et al., regarding the allowed set of prices.
Cite as

Georgios Amanatidis, Evangelos Markakis, and Krzysztof Sornat. Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{amanatidis_et_al:LIPIcs.MFCS.2016.9,
  author =	{Amanatidis, Georgios and Markakis, Evangelos and Sornat, Krzysztof},
  title =	{{Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{9:1--9:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.9},
  URN =		{urn:nbn:de:0030-drops-64254},
  doi =		{10.4230/LIPIcs.MFCS.2016.9},
  annote =	{Keywords: inequity aversion, social networks, revenue maximization}
}
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