8 Search Results for "Végh, László A."


Volume

LIPIcs, Volume 145

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

APPROX/RANDOM 2019, September 20-22, 2019, Massachusetts Institute of Technology, Cambridge, MA, USA

Editors: Dimitris Achlioptas and László A. Végh

Document
An Accelerated Newton-Dinkelbach Method and Its Application to Two Variables per Inequality Systems

Authors: Daniel Dadush, Zhuan Khye Koh, Bento Natura, and László A. Végh

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)


Abstract
We present an accelerated, or "look-ahead" version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current iterate and the optimal solution within every two iterations. Using the Bregman divergence as a potential in conjunction with combinatorial arguments, we obtain strongly polynomial algorithms in three applications domains: (i) For linear fractional combinatorial optimization, we show a convergence bound of O(mlog m) iterations; the previous best bound was O(m²log m) by Wang et al. (2006). (ii) We obtain a strongly polynomial label-correcting algorithm for solving linear feasibility systems with two variables per inequality (2VPI). For a 2VPI system with n variables and m constraints, our algorithm runs in O(mn) iterations. Every iteration takes O(mn) time for general 2VPI systems, and O(m + nlog n) time for the special case of deterministic Markov Decision Processes (DMDPs). This extends and strengthens a previous result by Madani (2002) that showed a weakly polynomial bound for a variant of the Newton–Dinkelbach method for solving DMDPs. (iii) We give a simplified variant of the parametric submodular function minimization result by Goemans et al. (2017).

Cite as

Daniel Dadush, Zhuan Khye Koh, Bento Natura, and László A. Végh. An Accelerated Newton-Dinkelbach Method and Its Application to Two Variables per Inequality Systems. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 36:1-36:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{dadush_et_al:LIPIcs.ESA.2021.36,
  author =	{Dadush, Daniel and Koh, Zhuan Khye and Natura, Bento and V\'{e}gh, L\'{a}szl\'{o} A.},
  title =	{{An Accelerated Newton-Dinkelbach Method and Its Application to Two Variables per Inequality Systems}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{36:1--36:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.36},
  URN =		{urn:nbn:de:0030-drops-146172},
  doi =		{10.4230/LIPIcs.ESA.2021.36},
  annote =	{Keywords: Newton-Dinkelbach method, fractional optimization, parametric optimization, strongly polynomial algorithms, two variables per inequality systems, Markov decision processes, submodular function minimization}
}
Document
Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications

Authors: Jugal Garg, Edin Husić, and László A. Végh

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


Abstract
We consider the Arrow-Debreu exchange market model where agents' demands satisfy the weak gross substitutes (WGS) property. This is a well-studied property, in particular, it gives a sufficient condition for the convergence of the classical tâtonnement dynamics. In this paper, we present a simple auction algorithm that obtains an approximate market equilibrium for WGS demands. Such auction algorithms have been previously known for restricted classes of WGS demands only. As an application of our technique, we obtain an efficient algorithm to find an approximate spending-restricted market equilibrium for WGS demands, a model that has been recently introduced as a continuous relaxation of the Nash social welfare (NSW) problem. This leads to a polynomial-time constant factor approximation algorithm for NSW with budget separable piecewise linear utility functions; only a pseudopolynomial approximation algorithm was known for this setting previously.

Cite as

Jugal Garg, Edin Husić, and László A. Végh. Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{garg_et_al:LIPIcs.STACS.2021.33,
  author =	{Garg, Jugal and Husi\'{c}, Edin and V\'{e}gh, L\'{a}szl\'{o} A.},
  title =	{{Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{33:1--33:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.33},
  URN =		{urn:nbn:de:0030-drops-136786},
  doi =		{10.4230/LIPIcs.STACS.2021.33},
  annote =	{Keywords: auction algorithm, weak gross substitutes, Fisher equilibrium, Gale equilibrium, Nash social welfare}
}
Document
Signed Tropical Convexity

Authors: Georg Loho and László A. Végh

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)


Abstract
We establish a new notion of tropical convexity for signed tropical numbers. We provide several equivalent descriptions involving balance relations and intersections of open halfspaces as well as the image of a union of polytopes over Puiseux series and hyperoperations. Along the way, we deduce a new Farkas' lemma and Fourier-Motzkin elimination without the non-negativity restriction on the variables. This leads to a Minkowski-Weyl theorem for polytopes over the signed tropical numbers.

Cite as

Georg Loho and László A. Végh. Signed Tropical Convexity. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 24:1-24:35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{loho_et_al:LIPIcs.ITCS.2020.24,
  author =	{Loho, Georg and V\'{e}gh, L\'{a}szl\'{o} A.},
  title =	{{Signed Tropical Convexity}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{24:1--24:35},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.24},
  URN =		{urn:nbn:de:0030-drops-117097},
  doi =		{10.4230/LIPIcs.ITCS.2020.24},
  annote =	{Keywords: tropical convexity, signed tropical numbers, Farkas' lemma}
}
Document
Complete Volume
LIPIcs, Volume 145, APPROX/RANDOM'19, Complete Volume

Authors: Dimitris Achlioptas and László A. Végh

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)


Abstract
LIPIcs, Volume 145, APPROX/RANDOM'19, Complete Volume

Cite as

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@Proceedings{achlioptas_et_al:LIPIcs.APPROX-RANDOM.2019,
  title =	{{LIPIcs, Volume 145, APPROX/RANDOM'19, Complete Volume}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019},
  URN =		{urn:nbn:de:0030-drops-113014},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019},
  annote =	{Keywords: Mathematics of computing; Theory of computation}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Dimitris Achlioptas and László A. Végh

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 0:i-0:xxii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{achlioptas_et_al:LIPIcs.APPROX-RANDOM.2019.0,
  author =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{0:i--0:xxii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.0},
  URN =		{urn:nbn:de:0030-drops-112155},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Paper
Algorithms for the Asymmetric Traveling Salesman Problem (Invited Paper)

Authors: Ola Svensson

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)


Abstract
The traveling salesman problem is one of the most fundamental optimization problems. Given n cities and pairwise distances, it is the problem of finding a tour of minimum total distance that visits each city once. In spite of significant research efforts, current techniques seem insufficient for settling the approximability of the traveling salesman problem. The gap in our understanding is especially large in the general asymmetric setting where the distance from city i to j is not assumed to equal the distance from j to i. Indeed, until recently, it remained an open problem to design an algorithm with any constant approximation guarantee. This status is particularly intriguing as the standard linear programming relaxation is believed to give a constant-factor approximation algorithm, where the constant may in fact be as small as 2. In this talk, we will give an overview of old and new approaches for settling this question. We shall, in particular, talk about our new approach that gives the first constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation. The main idea of our approach is to first give a generic reduction to structured instances and on those instances we then solve an easier problem (but equivalent in terms of constant-factor approximation) obtained by relaxing the general connectivity requirements into local connectivity conditions. This is based on joint work with Jakub Tarnawski and László A. Végh.

Cite as

Ola Svensson. Algorithms for the Asymmetric Traveling Salesman Problem (Invited Paper). In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{svensson:LIPIcs.FSTTCS.2018.3,
  author =	{Svensson, Ola},
  title =	{{Algorithms for the Asymmetric Traveling Salesman Problem}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.3},
  URN =		{urn:nbn:de:0030-drops-99024},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.3},
  annote =	{Keywords: Approximation algorithms, combinatorial optimization, linear programming, traveling salesman problem}
}
Document
A 7/3-Approximation for Feedback Vertex Sets in Tournaments

Authors: Matthias Mnich, Virginia Vassilevska Williams, and László A. Végh

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


Abstract
We consider the minimum-weight feedback vertex set problem in tournaments: given a tournament with non-negative vertex weights, remove a minimum-weight set of vertices that intersects all cycles. This problem is NP-hard to solve exactly, and Unique Games-hard to approximate by a factor better than 2. We present the first 7/3 approximation algorithm for this problem, improving on the previously best known ratio 5/2 given by Cai et al. [FOCS 1998, SICOMP 2001].

Cite as

Matthias Mnich, Virginia Vassilevska Williams, and László A. Végh. A 7/3-Approximation for Feedback Vertex Sets in Tournaments. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{mnich_et_al:LIPIcs.ESA.2016.67,
  author =	{Mnich, Matthias and Vassilevska Williams, Virginia and V\'{e}gh, L\'{a}szl\'{o} A.},
  title =	{{A 7/3-Approximation for Feedback Vertex Sets in Tournaments}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{67:1--67:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.67},
  URN =		{urn:nbn:de:0030-drops-64098},
  doi =		{10.4230/LIPIcs.ESA.2016.67},
  annote =	{Keywords: Approximation algorithms, feedback vertex sets, tournaments}
}
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