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Documents authored by Svensson, Ola

Document
Complete Volume
DOI: 10.4230/LIPIcs.ICALP.2024
LIPIcs, Volume 297, ICALP 2024, Complete Volume

Authors: Karl Bringmann, Martin Grohe, Gabriele Puppis, and Ola Svensson

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
LIPIcs, Volume 297, ICALP 2024, Complete Volume
Cite as

51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 1-2938, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Proceedings{bringmann_et_al:LIPIcs.ICALP.2024,
  title =	{{LIPIcs, Volume 297, ICALP 2024, Complete Volume}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{1--2938},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024},
  URN =		{urn:nbn:de:0030-drops-201424},
  doi =		{10.4230/LIPIcs.ICALP.2024},
  annote =	{Keywords: LIPIcs, Volume 297, ICALP 2024, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ICALP.2024.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Karl Bringmann, Martin Grohe, Gabriele Puppis, and Ola Svensson

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

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

51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 0:i-0:xl, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bringmann_et_al:LIPIcs.ICALP.2024.0,
  author =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{0:i--0:xl},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.0},
  URN =		{urn:nbn:de:0030-drops-201437},
  doi =		{10.4230/LIPIcs.ICALP.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/DagRep.13.2.1
Scheduling (Dagstuhl Seminar 23061)

Authors: Nicole Megow, Benjamin J. Moseley, David Shmoys, Ola Svensson, Sergei Vassilvitskii, and Jens Schlöter

Published in: Dagstuhl Reports, Volume 13, Issue 2 (2023)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23061 "Scheduling". The seminar focused on the emerging models for beyond-worst case algorithm design, in particular, recent approaches that incorporate learning. This includes models for the integration of learning into algorithm design that have been proposed recently and that have already demonstrated advances in the state-of-art for various scheduling applications: (i) scheduling with error-prone learned predictions, (ii) data-driven algorithm design, and (iii) stochastic and Bayesian learning in scheduling.
Cite as

Nicole Megow, Benjamin J. Moseley, David Shmoys, Ola Svensson, Sergei Vassilvitskii, and Jens Schlöter. Scheduling (Dagstuhl Seminar 23061). In Dagstuhl Reports, Volume 13, Issue 2, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{megow_et_al:DagRep.13.2.1,
  author =	{Megow, Nicole and Moseley, Benjamin J. and Shmoys, David and Svensson, Ola and Vassilvitskii, Sergei and Schl\"{o}ter, Jens},
  title =	{{Scheduling (Dagstuhl Seminar 23061)}},
  pages =	{1--19},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{2},
  editor =	{Megow, Nicole and Moseley, Benjamin J. and Shmoys, David and Svensson, Ola and Vassilvitskii, Sergei and Schl\"{o}ter, Jens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.2.1},
  URN =		{urn:nbn:de:0030-drops-191789},
  doi =		{10.4230/DagRep.13.2.1},
  annote =	{Keywords: scheduling, mathematical optimization, approximation algorithms, learning methods, uncertainty}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.52
Submodular Maximization Subject to Matroid Intersection on the Fly

Authors: Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Despite a surge of interest in submodular maximization in the data stream model, there remain significant gaps in our knowledge about what can be achieved in this setting, especially when dealing with multiple constraints. In this work, we nearly close several basic gaps in submodular maximization subject to k matroid constraints in the data stream model. We present a new hardness result showing that super polynomial memory in k is needed to obtain an o(k/(log k))-approximation. This implies near optimality of prior algorithms. For the same setting, we show that one can nevertheless obtain a constant-factor approximation by maintaining a set of elements whose size is independent of the stream size. Finally, for bipartite matching constraints, a well-known special case of matroid intersection, we present a new technique to obtain hardness bounds that are significantly stronger than those obtained with prior approaches. Prior results left it open whether a 2-approximation may exist in this setting, and only a complexity-theoretic hardness of 1.91 was known. We prove an unconditional hardness of 2.69.
Cite as

Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen. Submodular Maximization Subject to Matroid Intersection on the Fly. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{feldman_et_al:LIPIcs.ESA.2022.52,
  author =	{Feldman, Moran and Norouzi-Fard, Ashkan and Svensson, Ola and Zenklusen, Rico},
  title =	{{Submodular Maximization Subject to Matroid Intersection on the Fly}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{52:1--52:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.52},
  URN =		{urn:nbn:de:0030-drops-169902},
  doi =		{10.4230/LIPIcs.ESA.2022.52},
  annote =	{Keywords: Submodular Maximization, Matroid Intersection, Streaming Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.59
Streaming Submodular Maximization Under Matroid Constraints

Authors: Moran Feldman, Paul Liu, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Recent progress in (semi-)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural generalizations, including matroid constraints. This paper aims at closing this gap. For a single matroid of rank k (i.e., any solution has cardinality at most k), our main results are: - A single-pass streaming algorithm that uses Õ(k) memory and achieves an approximation guarantee of 0.3178. - A multi-pass streaming algorithm that uses Õ(k) memory and achieves an approximation guarantee of (1-1/e - ε) by taking a constant (depending on ε) number of passes over the stream. This improves on the previously best approximation guarantees of 1/4 and 1/2 for single-pass and multi-pass streaming algorithms, respectively. In fact, our multi-pass streaming algorithm is tight in that any algorithm with a better guarantee than 1/2 must make several passes through the stream and any algorithm that beats our guarantee of 1-1/e must make linearly many passes (as well as an exponential number of value oracle queries). Moreover, we show how the approach we use for multi-pass streaming can be further strengthened if the elements of the stream arrive in uniformly random order, implying an improved result for p-matchoid constraints.
Cite as

Moran Feldman, Paul Liu, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen. Streaming Submodular Maximization Under Matroid Constraints. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{feldman_et_al:LIPIcs.ICALP.2022.59,
  author =	{Feldman, Moran and Liu, Paul and Norouzi-Fard, Ashkan and Svensson, Ola and Zenklusen, Rico},
  title =	{{Streaming Submodular Maximization Under Matroid Constraints}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{59:1--59:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.59},
  URN =		{urn:nbn:de:0030-drops-164007},
  doi =		{10.4230/LIPIcs.ICALP.2022.59},
  annote =	{Keywords: Submodular maximization, streaming, matroid, random order}
}
Document
DOI: 10.4230/DagRep.10.2.50
Scheduling (Dagstuhl Seminar 20081)

Authors: Nicole Megow, David Shmoys, and Ola Svensson

Published in: Dagstuhl Reports, Volume 10, Issue 2 (2020)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 20081 "Scheduling". The seminar focused on the interplay between scheduling problems and problems that arise in the management of transportation and traffic. Important aspects at the intersection of these two research directions include data-driven approaches in dynamic decision-making, scheduling in combination with routing, shared mobility, and coordination versus competition.
Cite as

Nicole Megow, David Shmoys, and Ola Svensson. Scheduling (Dagstuhl Seminar 20081). In Dagstuhl Reports, Volume 10, Issue 2, pp. 50-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{megow_et_al:DagRep.10.2.50,
  author =	{Megow, Nicole and Shmoys, David and Svensson, Ola},
  title =	{{Scheduling (Dagstuhl Seminar 20081)}},
  pages =	{50--75},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{10},
  number =	{2},
  editor =	{Megow, Nicole and Shmoys, David and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.10.2.50},
  URN =		{urn:nbn:de:0030-drops-130590},
  doi =		{10.4230/DagRep.10.2.50},
  annote =	{Keywords: scheduling, optimization, approximation algorithms, routing, transportation, mechanism design}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.56
Robust Algorithms Under Adversarial Injections

Authors: Paritosh Garg, Sagar Kale, Lars Rohwedder, and Ola Svensson

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
In this paper, we study streaming and online algorithms in the context of randomness in the input. For several problems, a random order of the input sequence - as opposed to the worst-case order - appears to be a necessary evil in order to prove satisfying guarantees. However, algorithmic techniques that work under this assumption tend to be vulnerable to even small changes in the distribution. For this reason, we propose a new adversarial injections model, in which the input is ordered randomly, but an adversary may inject misleading elements at arbitrary positions. We believe that studying algorithms under this much weaker assumption can lead to new insights and, in particular, more robust algorithms. We investigate two classical combinatorial-optimization problems in this model: Maximum matching and cardinality constrained monotone submodular function maximization. Our main technical contribution is a novel streaming algorithm for the latter that computes a 0.55-approximation. While the algorithm itself is clean and simple, an involved analysis shows that it emulates a subdivision of the input stream which can be used to greatly limit the power of the adversary.
Cite as

Paritosh Garg, Sagar Kale, Lars Rohwedder, and Ola Svensson. Robust Algorithms Under Adversarial Injections. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 56:1-56:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{garg_et_al:LIPIcs.ICALP.2020.56,
  author =	{Garg, Paritosh and Kale, Sagar and Rohwedder, Lars and Svensson, Ola},
  title =	{{Robust Algorithms Under Adversarial Injections}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{56:1--56:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.56},
  URN =		{urn:nbn:de:0030-drops-124632},
  doi =		{10.4230/LIPIcs.ICALP.2020.56},
  annote =	{Keywords: Streaming algorithm, adversary, submodular maximization, matching}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ESA.2019
LIPIcs, Volume 144, ESA'19, Complete Volume

Authors: Michael A. Bender, Ola Svensson, and Grzegorz Herman

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
LIPIcs, Volume 144, ESA'19, Complete Volume
Cite as

27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{bender_et_al:LIPIcs.ESA.2019,
  title =	{{LIPIcs, Volume 144, ESA'19, Complete Volume}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019},
  URN =		{urn:nbn:de:0030-drops-113004},
  doi =		{10.4230/LIPIcs.ESA.2019},
  annote =	{Keywords: Applied computing, Transportation; Computing methodologies, Algebraic algorithms; Hardware, External storage; Human-centered computing, Graph drawings}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ESA.2019.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Michael A. Bender, Ola Svensson, and Grzegorz Herman

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

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

27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bender_et_al:LIPIcs.ESA.2019.0,
  author =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.0},
  URN =		{urn:nbn:de:0030-drops-111215},
  doi =		{10.4230/LIPIcs.ESA.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2019.3
Approximately Good and Modern Matchings (Invited Talk)

Authors: Ola Svensson

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
The matching problem is one of our favorite benchmark problems. Work on it has contributed to the development of many core concepts of computer science, including the equation of efficiency with polynomial time computation in the groundbreaking work by Edmonds in 1965. However, half a century later, we still do not have full understanding of the complexity of the matching problem in several models of computation such as parallel, online, and streaming algorithms. In this talk we survey some of the major challenges and report some recent progress.
Cite as

Ola Svensson. Approximately Good and Modern Matchings (Invited Talk). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{svensson:LIPIcs.ICALP.2019.3,
  author =	{Svensson, Ola},
  title =	{{Approximately Good and Modern Matchings}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.3},
  URN =		{urn:nbn:de:0030-drops-105797},
  doi =		{10.4230/LIPIcs.ICALP.2019.3},
  annote =	{Keywords: Algorithms, Matchings, Computational Complexity}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.FSTTCS.2018.3
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.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
DOI: 10.4230/LIPIcs.ICALP.2018.57
Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering

Authors: Buddhima Gamlath, Sangxia Huang, and Ola Svensson

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

Abstract
We study k-means clustering in a semi-supervised setting. Given an oracle that returns whether two given points belong to the same cluster in a fixed optimal clustering, we investigate the following question: how many oracle queries are sufficient to efficiently recover a clustering that, with probability at least (1 - delta), simultaneously has a cost of at most (1 + epsilon) times the optimal cost and an accuracy of at least (1 - epsilon)? We show how to achieve such a clustering on n points with O{((k^2 log n) * m{(Q, epsilon^4, delta / (k log n))})} oracle queries, when the k clusters can be learned with an epsilon' error and a failure probability delta' using m(Q, epsilon',delta') labeled samples in the supervised setting, where Q is the set of candidate cluster centers. We show that m(Q, epsilon', delta') is small both for k-means instances in Euclidean space and for those in finite metric spaces. We further show that, for the Euclidean k-means instances, we can avoid the dependency on n in the query complexity at the expense of an increased dependency on k: specifically, we give a slightly more involved algorithm that uses O{(k^4/(epsilon^2 delta) + (k^{9}/epsilon^4) log(1/delta) + k * m{({R}^r, epsilon^4/k, delta)})} oracle queries. We also show that the number of queries needed for (1 - epsilon)-accuracy in Euclidean k-means must linearly depend on the dimension of the underlying Euclidean space, and for finite metric space k-means, we show that it must at least be logarithmic in the number of candidate centers. This shows that our query complexities capture the right dependencies on the respective parameters.
Cite as

Buddhima Gamlath, Sangxia Huang, and Ola Svensson. Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 57:1-57:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{gamlath_et_al:LIPIcs.ICALP.2018.57,
  author =	{Gamlath, Buddhima and Huang, Sangxia and Svensson, Ola},
  title =	{{Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{57:1--57:14},
  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.2018.57},
  URN =		{urn:nbn:de:0030-drops-90612},
  doi =		{10.4230/LIPIcs.ICALP.2018.57},
  annote =	{Keywords: Clustering, Semi-supervised Learning, Approximation Algorithms, k-Means, k-Median}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2016.2
Algorithms with Provable Guarantees for Clustering (Invited Talk)

Authors: Ola Svensson

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

Abstract
In this talk, we give an overview of the current best approximation algorithms for fundamental clustering problems, such as k-center, k-median, k-means, and facility location. We focus on recent progress and point out several important open problems. For the uncapacitated versions, a variety of algorithmic methodologies, such as LP-rounding and primal-dual method, have been applied to a standard linear programming relaxation. This has given a uniform way of addressing these problems resulting in small constant approximation guarantees. In spite of this impressive progress, it remains a challenging open problem to give tight guarantees. Moreover, this collection of powerful algorithmic techniques is not easily applicable to the capacitated setting. In fact, there is no simple strong convex relaxation known for the capacitated versions. As a result, our understanding of these problems is significantly weaker and several fundamental questions remain open.
Cite as

Ola Svensson. Algorithms with Provable Guarantees for Clustering (Invited Talk). In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{svensson:LIPIcs.ESA.2016.2,
  author =	{Svensson, Ola},
  title =	{{Algorithms with Provable Guarantees for Clustering}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{2:1--2:1},
  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.2016.2},
  URN =		{urn:nbn:de:0030-drops-63435},
  doi =		{10.4230/LIPIcs.ESA.2016.2},
  annote =	{Keywords: Approximation algorithms, clustering}
}
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