161 Search Results for "Rabani, Yuval"

Volume

LIPIcs, Volume 55

43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

ICALP 2016, July 11-15, 2016, Rome, Italy

Editors: Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.16
Min-Sum Clustering (With Outliers)

Authors: Sandip Banerjee, Rafail Ostrovsky, and Yuval Rabani

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to compute a solution that clusters 98% of the input data points and pays no more than a constant factor times the optimal solution that clusters 99% of the input data points. More generally, we give the following bicriteria approximation: For any ε > 0, for any instance with n input points and for any positive integer n' ≤ n, we compute in polynomial time a clustering of at least (1-ε) n' points of cost at most a constant factor greater than the optimal cost of clustering n' points. The approximation guarantee grows with 1/(ε). Our results apply to instances of points in real space endowed with squared Euclidean distance, as well as to points in a metric space, where the number of clusters, and also the dimension if relevant, is arbitrary (part of the input, not an absolute constant).
Cite as

Sandip Banerjee, Rafail Ostrovsky, and Yuval Rabani. Min-Sum Clustering (With Outliers). In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{banerjee_et_al:LIPIcs.APPROX/RANDOM.2021.16,
  author =	{Banerjee, Sandip and Ostrovsky, Rafail and Rabani, Yuval},
  title =	{{Min-Sum Clustering (With Outliers)}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.16},
  URN =		{urn:nbn:de:0030-drops-147093},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.16},
  annote =	{Keywords: Clustering, approximation algorithms, primal-dual}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.37
Approximation Algorithms for Clustering with Dynamic Points

Authors: Shichuan Deng, Jian Li, and Yuval Rabani

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
In many classic clustering problems, we seek to sketch a massive data set of n points (a.k.a clients) in a metric space, by segmenting them into k categories or clusters, each cluster represented concisely by a single point in the metric space (a.k.a. the cluster’s center or its facility). The goal is to find such a sketch that minimizes some objective that depends on the distances between the clients and their respective facilities (the objective is a.k.a. the service cost). Two notable examples are the k-center/k-supplier problem where the objective is to minimize the maximum distance from any client to its facility, and the k-median problem where the objective is to minimize the sum over all clients of the distance from the client to its facility. In practical applications of clustering, the data set may evolve over time, reflecting an evolution of the underlying clustering model. Thus, in such applications, a good clustering must simultaneously represent the temporal data set well, but also not change too drastically between time steps. In this paper, we initiate the study of a dynamic version of clustering problems that aims to capture these considerations. In this version there are T time steps, and in each time step t ∈ {1,2,… ,T}, the set of clients needed to be clustered may change, and we can move the k facilities between time steps. The general goal is to minimize certain combinations of the service cost and the facility movement cost, or minimize one subject to some constraints on the other. More specifically, we study two concrete problems in this framework: the Dynamic Ordered k-Median and the Dynamic k-Supplier problem. Our technical contributions are as follows: - We consider the Dynamic Ordered k-Median problem, where the objective is to minimize the weighted sum of ordered distances over all time steps, plus the total cost of moving the facilities between time steps. We present one constant-factor approximation algorithm for T = 2 and another approximation algorithm for fixed T ≥ 3. - We consider the Dynamic k-Supplier problem, where the objective is to minimize the maximum distance from any client to its facility, subject to the constraint that between time steps the maximum distance moved by any facility is no more than a given threshold. When the number of time steps T is 2, we present a simple constant factor approximation algorithm and a bi-criteria constant factor approximation algorithm for the outlier version, where some of the clients can be discarded. We also show that it is NP-hard to approximate the problem with any factor for T ≥ 3.
Cite as

Shichuan Deng, Jian Li, and Yuval Rabani. Approximation Algorithms for Clustering with Dynamic Points. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{deng_et_al:LIPIcs.ESA.2020.37,
  author =	{Deng, Shichuan and Li, Jian and Rabani, Yuval},
  title =	{{Approximation Algorithms for Clustering with Dynamic Points}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.37},
  URN =		{urn:nbn:de:0030-drops-129037},
  doi =		{10.4230/LIPIcs.ESA.2020.37},
  annote =	{Keywords: clustering, dynamic points, multi-objective optimization}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.54
Parametrized Metrical Task Systems

Authors: Sébastien Bubeck and Yuval Rabani

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
We consider parametrized versions of metrical task systems and metrical service systems, two fundamental models of online computing, where the constrained parameter is the number of possible distinct requests m. Such parametrization occurs naturally in a wide range of applications. Striking examples are certain power management problems, which are modeled as metrical task systems with m = 2. We characterize the competitive ratio in terms of the parameter m for both deterministic and randomized algorithms on hierarchically separated trees. Our findings uncover a rich and unexpected picture that differs substantially from what is known or conjectured about the unparametrized versions of these problems. For metrical task systems, we show that deterministic algorithms do not exhibit any asymptotic gain beyond one-level trees (namely, uniform metric spaces), whereas randomized algorithms do not exhibit any asymptotic gain even for one-level trees. In contrast, the special case of metrical service systems (subset chasing) behaves very differently. Both deterministic and randomized algorithms exhibit gain, for m sufficiently small compared to n, for any number of levels. Most significantly, they exhibit a large gain for uniform metric spaces and a smaller gain for two-level trees. Moreover, it turns out that in these cases (as well as in the case of metrical task systems for uniform metric spaces with m being an absolute constant), deterministic algorithms are essentially as powerful as randomized algorithms. This is surprising and runs counter to the ubiquitous intuition/conjecture that, for most problems that can be modeled as metrical task systems, the randomized competitive ratio is polylogarithmic in the deterministic competitive ratio.
Cite as

Sébastien Bubeck and Yuval Rabani. Parametrized Metrical Task Systems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 54:1-54:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bubeck_et_al:LIPIcs.APPROX/RANDOM.2020.54,
  author =	{Bubeck, S\'{e}bastien and Rabani, Yuval},
  title =	{{Parametrized Metrical Task Systems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{54:1--54:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.54},
  URN =		{urn:nbn:de:0030-drops-126573},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.54},
  annote =	{Keywords: online computing, competitive analysis, metrical task systems}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.93
Strictly Balancing Matrices in Polynomial Time Using Osborne's Iteration

Authors: Rafail Ostrovsky, Yuval Rabani, and Arman Yousefi

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

Abstract
Osborne's iteration is a method for balancing n x n matrices which is widely used in linear algebra packages, as balancing preserves eigenvalues and stabilizes their numeral computation. The iteration can be implemented in any norm over R^n, but it is normally used in the L_2 norm. The choice of norm not only affects the desired balance condition, but also defines the iterated balancing step itself. In this paper we focus on Osborne's iteration in any L_p norm, where p < infty. We design a specific implementation of Osborne's iteration in any L_p norm that converges to a strictly epsilon-balanced matrix in O~(epsilon^{-2}n^{9} K) iterations, where K measures, roughly, the number of bits required to represent the entries of the input matrix. This is the first result that proves a variant of Osborne's iteration in the L_2 norm (or any L_p norm, p < infty) strictly balances matrices in polynomial time. This is a substantial improvement over our recent result (in SODA 2017) that showed weak balancing in L_p norms. Previously, Schulman and Sinclair (STOC 2015) showed strict balancing of another variant of Osborne's iteration in the L_infty norm. Their result does not imply any bounds on strict balancing in other norms.
Cite as

Rafail Ostrovsky, Yuval Rabani, and Arman Yousefi. Strictly Balancing Matrices in Polynomial Time Using Osborne's Iteration. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 93:1-93:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ostrovsky_et_al:LIPIcs.ICALP.2018.93,
  author =	{Ostrovsky, Rafail and Rabani, Yuval and Yousefi, Arman},
  title =	{{Strictly Balancing Matrices in Polynomial Time Using Osborne's Iteration}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{93:1--93:11},
  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.2018.93},
  URN =		{urn:nbn:de:0030-drops-90976},
  doi =		{10.4230/LIPIcs.ICALP.2018.93},
  annote =	{Keywords: Numerical Linear Algebra, Optimization}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.21
Approximating Sparsest Cut in Low Rank Graphs via Embeddings from Approximately Low Dimensional Spaces

Authors: Yuval Rabani and Rakesh Venkat

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
We consider the problem of embedding a finite set of points x_1, ... , x_n in R^d that satisfy l_2^2 triangle inequalities into l_1, when the points are approximately low-dimensional. Goemans (unpublished, appears in a work of Magen and Moharammi (2008) ) showed that such points residing in exactly d dimensions can be embedded into l_1 with distortion at most sqrt{d}. We prove the following robust analogue of this statement: if there exists a r-dimensional subspace Pi such that the projections onto this subspace satisfy sum_{i,j in [n]} norm{Pi x_i - Pi x_j}_2^2 >= Omega(1) * sum_{i,j \in [n]} norm{x_i - x_j}_2^2, then there is an embedding of the points into l_1 with O(sqrt{r}) average distortion. A consequence of this result is that the integrality gap of the well-known Goemans-Linial SDP relaxation for the Uniform Sparsest Cut problem is O(sqrt{r}) on graphs G whose r-th smallest normalized eigenvalue of the Laplacian satisfies lambda_r(G)/n >= Omega(1)*Phi_{SDP}(G). Our result improves upon the previously known bound of O(r) on the average distortion, and the integrality gap of the Goemans-Linial SDP under the same preconditions, proven in [Deshpande and Venkat, 2014], and [Deshpande, Harsha and Venkat 2016].
Cite as

Yuval Rabani and Rakesh Venkat. Approximating Sparsest Cut in Low Rank Graphs via Embeddings from Approximately Low Dimensional Spaces. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{rabani_et_al:LIPIcs.APPROX-RANDOM.2017.21,
  author =	{Rabani, Yuval and Venkat, Rakesh},
  title =	{{Approximating Sparsest Cut in Low Rank Graphs via Embeddings from Approximately Low Dimensional Spaces}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.21},
  URN =		{urn:nbn:de:0030-drops-75705},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.21},
  annote =	{Keywords: Metric Embeddings, Sparsest Cut, Negative type metrics, Approximation Algorithms}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ICALP.2016
LIPIcs, Volume 55, ICALP'16, Complete Volume

Authors: Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
LIPIcs, Volume 55, ICALP'16, Complete Volume
Cite as

43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Proceedings{chatzigiannakis_et_al:LIPIcs.ICALP.2016,
  title =	{{LIPIcs, Volume 55, ICALP'16, Complete Volume}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016},
  URN =		{urn:nbn:de:0030-drops-65844},
  doi =		{10.4230/LIPIcs.ICALP.2016},
  annote =	{Keywords: Theory of Computation}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ICALP.2016.0
Front Matter, Table of Contents, Preface, Organization, List of Authors

Authors: Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Front Matter, Table of Contents, Preface, Organization, List of Authors
Cite as

43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 0:i-0:xliv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chatzigiannakis_et_al:LIPIcs.ICALP.2016.0,
  author =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  title =	{{Front Matter, Table of Contents, Preface, Organization, List of Authors}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{0:i--0:xliv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.0},
  URN =		{urn:nbn:de:0030-drops-61917},
  doi =		{10.4230/LIPIcs.ICALP.2016.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Organization, List of Authors}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2016.1
Compute Choice (Invited Talk)

Authors: Devavrat Shah

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
In this talk, we shall discuss the question of learning distribution over permutations of n choices based on partial observations. This is central to capturing the so called "choice" in a variety of contexts: understanding preferences of consumers over a collection of products based on purchasing and browsing data in the setting of retail and e-commerce, learning public opinion amongst a collection of socio-economic issues based on sparse polling data, and deciding a ranking of teams or players based on outcomes of games. The talk will primarily discuss the relationship between the ability to learn, nature of partial information and number of available observations. Connections to the classical theory of social choice and behavioral psychology, as well as modern literature in Statistics, learning theory and operations research will be discussed.
Cite as

Devavrat Shah. Compute Choice (Invited Talk). In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{shah:LIPIcs.ICALP.2016.1,
  author =	{Shah, Devavrat},
  title =	{{Compute Choice}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.1},
  URN =		{urn:nbn:de:0030-drops-63374},
  doi =		{10.4230/LIPIcs.ICALP.2016.1},
  annote =	{Keywords: Decision Systems, Learning Distributions, Partial observations}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2016.2
Formally Verifying a Compiler: What Does It Mean, Exactly? (Invited Talk)

Authors: Xavier Leroy

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Compilers, and especially optimizing compilers, are complicated programs. Bugs in compilers happen, and can lead to miscompilation: the production of wrong executable code from a correct source program. Miscompilation is documented in the literature and a concern for high-assurance software, as it endangers the guarantees obtained by source-level formal verification of programs. Compiler verification is a radical solution to the miscompilation problem: by applying program proof to the compiler itself, we can obtain mathematically strong guarantees that the generated executable code is faithful to the semantics of the source program. The state of the art in this line of research is arguably the CompCert verified compiler. This talk will give an overview of this optimizing C compiler and of its formal verification, conducted with the Coq proof assistant. A formal verification is as good as the specifications it uses. In other words, verification reduces the problem of trusting a large implementation to that of ensuring that its formal specification enforce the intended correctness properties. In the case of CompCert, the correctness statement that is proved is rather complex, as it involves large operational semantics (for the C language and for the assembly languages of the target architectures) and simulations between these semantics that support both choice refinement and behavior refinement. The talk will review and discuss these elements of the specification, along with some of the accompanying proof principles.
Cite as

Xavier Leroy. Formally Verifying a Compiler: What Does It Mean, Exactly? (Invited Talk). In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{leroy:LIPIcs.ICALP.2016.2,
  author =	{Leroy, Xavier},
  title =	{{Formally Verifying a Compiler: What Does It Mean, Exactly?}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.2},
  URN =		{urn:nbn:de:0030-drops-63384},
  doi =		{10.4230/LIPIcs.ICALP.2016.2},
  annote =	{Keywords: Compilers, Compiler Optimization, Compiler Verification}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2016.3
Hardness of Approximation (Invited Talk)

Authors: Subhash Khot

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
The talk will present connections between approximability of NP-complete problems, analysis, and geometry, and the role played by the Unique Games Conjecture in facilitating these connections.
Cite as

Subhash Khot. Hardness of Approximation (Invited Talk). In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{khot:LIPIcs.ICALP.2016.3,
  author =	{Khot, Subhash},
  title =	{{Hardness of Approximation}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.3},
  URN =		{urn:nbn:de:0030-drops-63395},
  doi =		{10.4230/LIPIcs.ICALP.2016.3},
  annote =	{Keywords: NP-completeness, Approximation algorithms, Inapproximability, Probabilistically Checkable Proofs, Discrete Fourier analysis}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2016.4
Model Checking and Strategy Synthesis for Stochastic Games: From Theory to Practice (Invited Talk)

Authors: Marta Z. Kwiatkowska

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Probabilistic model checking is an automatic procedure for establishing if a desired property holds in a probabilistic model, aimed at verifying quantitative probabilistic specifications such as the probability of a critical failure occurring or expected time to termination. Much progress has been made in recent years in algorithms, tools and applications of probabilistic model checking, as exemplified by the probabilistic model checker PRISM (http://www.prismmodelchecker.org). However, the unstoppable rise of autonomous systems, from robotic assistants to self-driving cars, is placing greater and greater demands on quantitative modelling and verification technologies. To address the challenges of autonomy we need to consider collaborative, competitive and adversarial behaviour, which is naturally modelled using game-theoretic abstractions, enhanced with stochasticity arising from randomisation and uncertainty. This paper gives an overview of quantitative verification and strategy synthesis techniques developed for turn-based stochastic multi-player games, summarising recent advances concerning multi-objective properties and compositional strategy synthesis. The techniques have been implemented in the PRISM-games model checker built as an extension of PRISM.
Cite as

Marta Z. Kwiatkowska. Model Checking and Strategy Synthesis for Stochastic Games: From Theory to Practice (Invited Talk). In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{kwiatkowska:LIPIcs.ICALP.2016.4,
  author =	{Kwiatkowska, Marta Z.},
  title =	{{Model Checking and Strategy Synthesis for Stochastic Games: From Theory to Practice}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.4},
  URN =		{urn:nbn:de:0030-drops-62285},
  doi =		{10.4230/LIPIcs.ICALP.2016.4},
  annote =	{Keywords: Quantitative verification, Stochastic games, Temporal logic, Model checking, Strategy synthesis}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.5
Fine-Grained Complexity Analysis of Two Classic TSP Variants

Authors: Mark de Berg, Kevin Buchin, Bart M. P. Jansen, and Gerhard Woeginger

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We analyze two classic variants of the Traveling Salesman Problem using the toolkit of fine-grained complexity. Our first set of results is motivated by the Bitonic tsp problem: given a set of n points in the plane, compute a shortest tour consisting of two monotone chains. It is a classic dynamicprogramming exercise to solve this problem in O(n^2) time. While the near-quadratic dependency of similar dynamic programs for Longest Common Subsequence and Discrete Fréchet Distance has recently been proven to be essentially optimal under the Strong Exponential Time Hypothesis, we show that bitonic tours can be found in subquadratic time. More precisely, we present an algorithm that solves bitonic tsp in O(n*log^2(n)) time and its bottleneck version in O(n*log^3(n)) time. In the more general pyramidal tsp problem, the points to be visited are labeled 1, ..., n and the sequence of labels in the solution is required to have at most one local maximum. Our algorithms for the bitonic (bottleneck) tsp problem also work for the pyramidal tsp problem in the plane. Our second set of results concerns the popular k-opt heuristic for tsp in the graph setting. More precisely, we study the k-opt decision problem, which asks whether a given tour can be improved by a k-opt move that replaces k edges in the tour by k new edges. A simple algorithm solves k-opt in O(n^k) time for fixed k. For 2-opt, this is easily seen to be optimal. For k = 3 we prove that an algorithm with a runtime of the form ~O(n^{3-epsilon}) exists if and only if All-Pairs Shortest Paths in weighted digraphs has such an algorithm. For general k-opt, it is known that a runtime of f(k)*n^{o(k/log(k))} would contradict the Exponential Time Hypothesis. The results for k = 2, 3 may suggest that the actual time complexity of k-opt is Theta(n^k). We show that this is not the case, by presenting an algorithm that finds the best k-move in O(n^{lfoor 2k/3 rfloor +1}) time for fixed k >= 3. This implies that 4-opt can be solved in O(n^3) time, matching the best-known algorithm for 3-opt. Finally, we show how to beat the quadratic barrier for k = 2 in two important settings, namely for points in the plane and when we want to solve 2-opt repeatedly
Cite as

Mark de Berg, Kevin Buchin, Bart M. P. Jansen, and Gerhard Woeginger. Fine-Grained Complexity Analysis of Two Classic TSP Variants. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{deberg_et_al:LIPIcs.ICALP.2016.5,
  author =	{de Berg, Mark and Buchin, Kevin and Jansen, Bart M. P. and Woeginger, Gerhard},
  title =	{{Fine-Grained Complexity Analysis of Two Classic TSP Variants}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.5},
  URN =		{urn:nbn:de:0030-drops-62770},
  doi =		{10.4230/LIPIcs.ICALP.2016.5},
  annote =	{Keywords: Traveling salesman problem, fine-grained complexity, bitonic tours, k-opt}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.6
Bicovering: Covering Edges With Two Small Subsets of Vertices

Authors: Amey Bhangale, Rajiv Gandhi, Mohammad Taghi Hajiaghayi, Rohit Khandekar, and Guy Kortsarz

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We study the following basic problem called Bi-Covering. Given a graph G(V, E), find two (not necessarily disjoint) sets A subseteq V and B subseteq V such that A union B = V and that every edge e belongs to either the graph induced by A or to the graph induced by B. The goal is to minimize max{|A|, |B|}. This is the most simple case of the Channel Allocation problem [Gandhi et al., Networks, 2006]. A solution that outputs V,emptyset gives ratio at most 2. We show that under the similar Strong Unique Game Conjecture by [Bansal-Khot, FOCS, 2009] there is no 2 - epsilon ratio algorithm for the problem, for any constant epsilon > 0. Given a bipartite graph, Max-bi-clique is a problem of finding largest k*k complete bipartite sub graph. For Max-bi-clique problem, a constant factor hardness was known under random 3-SAT hypothesis of Feige [Feige, STOC, 2002] and also under the assumption that NP !subseteq intersection_{epsilon > 0} BPTIME(2^{n^{epsilon}}) [Khot, SIAM J. on Comp., 2011]. It was an open problem in [Ambühl et. al., SIAM J. on Comp., 2011] to prove inapproximability of Max-bi-clique assuming weaker conjecture. Our result implies similar hardness result assuming the Strong Unique Games Conjecture. On the algorithmic side, we also give better than 2 approximation for Bi-Covering on numerous special graph classes. In particular, we get 1.876 approximation for Chordal graphs, exact algorithm for Interval Graphs, 1 + o(1) for Minor Free Graph, 2 - 4*delta/3 for graphs with minimum degree delta*n, 2/(1+delta^2/8) for delta-vertex expander, 8/5 for Split Graphs, 2 - (6/5)*1/d for graphs with minimum constant degree d etc. Our algorithmic results are quite non-trivial. In achieving these results, we use various known structural results about the graphs, combined with the techniques that we develop tailored to getting better than 2 approximation.
Cite as

Amey Bhangale, Rajiv Gandhi, Mohammad Taghi Hajiaghayi, Rohit Khandekar, and Guy Kortsarz. Bicovering: Covering Edges With Two Small Subsets of Vertices. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bhangale_et_al:LIPIcs.ICALP.2016.6,
  author =	{Bhangale, Amey and Gandhi, Rajiv and Hajiaghayi, Mohammad Taghi and Khandekar, Rohit and Kortsarz, Guy},
  title =	{{Bicovering: Covering Edges With Two Small Subsets of Vertices}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.6},
  URN =		{urn:nbn:de:0030-drops-62728},
  doi =		{10.4230/LIPIcs.ICALP.2016.6},
  annote =	{Keywords: Bi-covering, Unique Games, Max Bi-clique}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.7
Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs

Authors: Chandra Chekuri, Alina Ene, and Marcin Pilipczuk

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We study the problem of routing symmetric demand pairs in planar digraphs. The input consists of a directed planar graph G = (V, E) and a collection of k source-destination pairs M = {s_1t_1, ..., s_kt_k}. The goal is to maximize the number of pairs that are routed along disjoint paths. A pair s_it_i is routed in the symmetric setting if there is a directed path connecting s_i to t_i and a directed path connecting t_i to s_i. In this paper we obtain a randomized poly-logarithmic approximation with constant congestion for this problem in planar digraphs. The main technical contribution is to show that a planar digraph with directed treewidth h contains a constant congestion crossbar of size Omega(h/polylog(h)).
Cite as

Chandra Chekuri, Alina Ene, and Marcin Pilipczuk. Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chekuri_et_al:LIPIcs.ICALP.2016.7,
  author =	{Chekuri, Chandra and Ene, Alina and Pilipczuk, Marcin},
  title =	{{Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.7},
  URN =		{urn:nbn:de:0030-drops-62737},
  doi =		{10.4230/LIPIcs.ICALP.2016.7},
  annote =	{Keywords: Disjoint paths, symmetric demands, planar directed graph}
}
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