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Volume

LIPIcs, Volume 87

25th Annual European Symposium on Algorithms (ESA 2017)

ESA 2017, September 4-6, 2017, Vienna, Austria

Editors: Kirk Pruhs and Christian Sohler

Document

Invited Talk

DOI: 10.4230/LIPIcs.ICDT.2022.1

On an Information Theoretic Approach to Cardinality Estimation (Invited Talk)

Authors: Hung Q. Ngo

Published in: LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

Abstract

This article is a companion to an invited talk at ICDT'2022 with the same title. Cardinality estimation is among the most important problems in query optimization. It is well-documented that, when query plans go haywire, in most cases one can trace the root cause to the cardinality estimator being far off. In particular, traditional cardinality estimation based on selectivity estimation may sometimes under-estimate cardinalities by orders of magnitudes, because the independence or the uniformity assumptions do not typically hold. This talk outlines an approach to cardinality estimation that is "model-free" from a statistical stand-point. Being model-free means the approach tries to avoid making any distributional assumptions. Our approach is information-theoretic, and generalizes recent results on worst-case output size bounds of queries, allowing the estimator to take into account histogram information from the input relations. The estimator turns out to be the objective of a maximization problem subject to concave constraints, over an exponential number of variables. We then explain how the estimator can be computed in polynomial time for some fragment of these constraints. Overall, the talk introduces a new direction to address the classic problem of cardinality estimation that is designed to circumvent some of the pitfalls of selectivity-based estimation. We will also explain connections to other fundamental problems in information theory and database theory regarding information inequalities. The talk is based on (published and unpublished) joint works with Mahmoud Abo Khamis, Sungjin Im, Hossein Keshavarz, Phokion Kolaitis, Ben Moseley, XuanLong Nguyen, Kirk Pruhs, Dan Suciu, and Alireza Samadian Zakaria

Cite as

Hung Q. Ngo. On an Information Theoretic Approach to Cardinality Estimation (Invited Talk). In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 1:1-1:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ngo:LIPIcs.ICDT.2022.1,
  author =	{Ngo, Hung Q.},
  title =	{{On an Information Theoretic Approach to Cardinality Estimation}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{1:1--1:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-223-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{220},
  editor =	{Olteanu, Dan and Vortmeier, Nils},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.1},
  URN =		{urn:nbn:de:0030-drops-158750},
  doi =		{10.4230/LIPIcs.ICDT.2022.1},
  annote =	{Keywords: Cardinality Estimation, Information Theory, Polymatroid Bound, Worst-case Optimal Join}
}

Document

DOI: 10.4230/LIPIcs.ESA.2021.62

An Efficient Reduction of a Gammoid to a Partition Matroid

Authors: Marilena Leichter, Benjamin Moseley, and Kirk Pruhs

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

Abstract

Our main contribution is a polynomial-time algorithm to reduce a k-colorable gammoid to a (2k-2)-colorable partition matroid. It is known that there are gammoids that can not be reduced to any (2k-3)-colorable partition matroid, so this result is tight. We then discuss how such a reduction can be used to obtain polynomial-time algorithms with better approximation ratios for various natural problems related to coloring and list coloring the intersection of matroids.

Cite as

Marilena Leichter, Benjamin Moseley, and Kirk Pruhs. An Efficient Reduction of a Gammoid to a Partition Matroid. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 62:1-62:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{leichter_et_al:LIPIcs.ESA.2021.62,
  author =	{Leichter, Marilena and Moseley, Benjamin and Pruhs, Kirk},
  title =	{{An Efficient Reduction of a Gammoid to a Partition Matroid}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{62:1--62:13},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.62},
  URN =		{urn:nbn:de:0030-drops-146432},
  doi =		{10.4230/LIPIcs.ESA.2021.62},
  annote =	{Keywords: Matroid, Gammoid, Reduction, Algorithms}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2021.6

An Approximation Algorithm for the Matrix Tree Multiplication Problem

Authors: Mahmoud Abo-Khamis, Ryan Curtin, Sungjin Im, Benjamin Moseley, Hung Ngo, Kirk Pruhs, and Alireza Samadian

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

We consider the Matrix Tree Multiplication problem. This problem is a generalization of the classic Matrix Chain Multiplication problem covered in the dynamic programming chapter of many introductory algorithms textbooks. An instance of the Matrix Tree Multiplication problem consists of a rooted tree with a matrix associated with each edge. The output is, for each leaf in the tree, the product of the matrices on the chain/path from the root to that leaf. Matrix multiplications that are shared between various chains need only be computed once, potentially being shared between different root to leaf chains. Algorithms are evaluated by the number of scalar multiplications performed. Our main result is a linear time algorithm for which the number of scalar multiplications performed is at most 15 times the optimal number of scalar multiplications.

Cite as

Mahmoud Abo-Khamis, Ryan Curtin, Sungjin Im, Benjamin Moseley, Hung Ngo, Kirk Pruhs, and Alireza Samadian. An Approximation Algorithm for the Matrix Tree Multiplication Problem. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 6:1-6:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{abokhamis_et_al:LIPIcs.MFCS.2021.6,
  author =	{Abo-Khamis, Mahmoud and Curtin, Ryan and Im, Sungjin and Moseley, Benjamin and Ngo, Hung and Pruhs, Kirk and Samadian, Alireza},
  title =	{{An Approximation Algorithm for the Matrix Tree Multiplication Problem}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.6},
  URN =		{urn:nbn:de:0030-drops-144464},
  doi =		{10.4230/LIPIcs.MFCS.2021.6},
  annote =	{Keywords: Matrix Multiplication, Approximation Algorithm}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2021.97

Relational Algorithms for k-Means Clustering

Authors: Benjamin Moseley, Kirk Pruhs, Alireza Samadian, and Yuyan Wang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows represent the data points. The running time is potentially exponentially smaller than N, the number of data points to be clustered that the relational database represents. Few relational algorithms are known and this paper offers techniques for designing relational algorithms as well as characterizing their limitations. We show that given two data points as cluster centers, if we cluster points according to their closest centers, it is NP-Hard to approximate the number of points in the clusters on a general relational input. This is trivial for conventional data inputs and this result exemplifies that standard algorithmic techniques may not be directly applied when designing an efficient relational algorithm. This paper then introduces a new method that leverages rejection sampling and the k-means++ algorithm to construct a O(1)-approximate k-means solution.

Cite as

Benjamin Moseley, Kirk Pruhs, Alireza Samadian, and Yuyan Wang. Relational Algorithms for k-Means Clustering. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 97:1-97:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{moseley_et_al:LIPIcs.ICALP.2021.97,
  author =	{Moseley, Benjamin and Pruhs, Kirk and Samadian, Alireza and Wang, Yuyan},
  title =	{{Relational Algorithms for k-Means Clustering}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{97:1--97:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.97},
  URN =		{urn:nbn:de:0030-drops-141668},
  doi =		{10.4230/LIPIcs.ICALP.2021.97},
  annote =	{Keywords: k-means, clustering, approximation, big-data, databases}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2021.103

Matching on the Line Admits No o(√log n)-Competitive Algorithm

Authors: Enoch Peserico and Michele Scquizzato

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

We present a simple proof that the competitive ratio of any randomized online matching algorithm for the line exceeds √{log₂(n +1)}/15 for all n = 2ⁱ-1: i ∈ ℕ, settling a 25-year-old open question.

Cite as

Enoch Peserico and Michele Scquizzato. Matching on the Line Admits No o(√log n)-Competitive Algorithm. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 103:1-103:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{peserico_et_al:LIPIcs.ICALP.2021.103,
  author =	{Peserico, Enoch and Scquizzato, Michele},
  title =	{{Matching on the Line Admits No o(√log n)-Competitive Algorithm}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{103:1--103:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.103},
  URN =		{urn:nbn:de:0030-drops-141720},
  doi =		{10.4230/LIPIcs.ICALP.2021.103},
  annote =	{Keywords: Metric matching, online algorithms, competitive analysis}
}

Document

Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management

DOI: 10.4230/LIPIcs.ICALP.2019.145

Matroid Coflow Scheduling

Authors: Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Manish Purohit

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

Abstract

We consider the matroid coflow scheduling problem, where each job is comprised of a set of flows and the family of sets that can be scheduled at any time form a matroid. Our main result is a polynomial-time algorithm that yields a 2-approximation for the objective of minimizing the weighted completion time. This result is tight assuming P != NP. As a by-product we also obtain the first (2+epsilon)-approximation algorithm for the preemptive concurrent open shop scheduling problem.

Cite as

Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Manish Purohit. Matroid Coflow Scheduling. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 145:1-145:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{im_et_al:LIPIcs.ICALP.2019.145,
  author =	{Im, Sungjin and Moseley, Benjamin and Pruhs, Kirk and Purohit, Manish},
  title =	{{Matroid Coflow Scheduling}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{145:1--145:13},
  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.2019.145},
  URN =		{urn:nbn:de:0030-drops-107213},
  doi =		{10.4230/LIPIcs.ICALP.2019.145},
  annote =	{Keywords: Coflow Scheduling, Concurrent Open Shop, Matroid Scheduling}
}

Document

DOI: 10.4230/LITES-v005-i001-a001

Risk-Aware Scheduling of Dual Criticality Job Systems Using Demand Distributions

Authors: Bader Naim Alahmad and Sathish Gopalakrishnan

Published in: LITES, Volume 5, Issue 1 (2018). Leibniz Transactions on Embedded Systems, Volume 5, Issue 1

Abstract

We pose the problem of scheduling Mixed Criticality (MC) job systems when there are only two criticality levels, Lo and Hi -referred to as Dual Criticality job systems- on a single processing platform, when job demands are probabilistic and their distributions are known. The current MC models require that the scheduling policy allocate as little execution time as possible to Lo-criticality jobs if the scenario of execution is of Hi criticality, and drop Lo-criticality jobs entirely as soon as the execution scenario's criticality level can be inferred and is Hi. The work incurred by "incorrectly" scheduling Lo-criticality jobs in cases of Hi realized scenarios might affect the feasibility of Hi criticality jobs; we quantify this work and call it Work Threatening Feasibility (WTF). Our objective is to construct online scheduling policies that minimize the expected WTF for the given instance, and under which the instance is feasible in a probabilistic sense that is consistent with the traditional deterministic definition of MC feasibility. We develop a probabilistic framework for MC scheduling, where feasibility is defined in terms of (chance) constraints on the probabilities that Lo and Hi jobs meet their deadlines. The probabilities are computed over the set of sample paths, or trajectories, induced by executing the policy, and those paths are dependent upon the set of execution scenarios and the given demand distributions. Our goal is to exploit the information provided by job distributions to compute the minimum expected WTF below which the given instance is not feasible in probability, and to compute a (randomized) "efficiently implementable" scheduling policy that realizes the latter quantity. We model the problem as a Constrained Markov Decision Process (CMDP) over a suitable state space and a finite planning horizon, and show that an optimal (non-stationary) Markov randomized scheduling policy exists. We derive an optimal policy by solving a Linear Program (LP). We also carry out quantitative evaluations on select probabilistic MC instances to demonstrate that our approach potentially outperforms current MC scheduling policies.

Cite as

Bader Naim Alahmad and Sathish Gopalakrishnan. Risk-Aware Scheduling of Dual Criticality Job Systems Using Demand Distributions. In LITES, Volume 5, Issue 1 (2018). Leibniz Transactions on Embedded Systems, Volume 5, Issue 1, pp. 01:1-01:30, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@Article{alahmad_et_al:LITES-v005-i001-a001,
  author =	{Alahmad, Bader Naim and Gopalakrishnan, Sathish},
  title =	{{Risk-Aware Scheduling of Dual Criticality Job Systems Using Demand Distributions}},
  booktitle =	{LITES, Volume 5, Issue 1 (2018)},
  pages =	{01:1--01:30},
  journal =	{Leibniz Transactions on Embedded Systems},
  ISSN =	{2199-2002},
  year =	{2018},
  volume =	{5},
  number =	{1},
  editor =	{Alahmad, Bader Naim and Gopalakrishnan, Sathish},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES-v005-i001-a001},
  doi =		{10.4230/LITES-v005-i001-a001},
  annote =	{Keywords: Mixed criticalities, Probability distribution, Real time systems, Scheduling, Chance constrained Markov decision process, Linear programming, Randomized policy}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.ESA.2017

LIPIcs, Volume 87, ESA'17, Complete Volume

Authors: Kirk Pruhs and Christian Sohler

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

LIPIcs, Volume 87, ESA'17, Complete Volume

Cite as

Kirk Pruhs and Christian Sohler. LIPIcs, Volume 87, ESA'17, Complete Volume. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@Proceedings{pruhs_et_al:LIPIcs.ESA.2017,
  title =	{{LIPIcs, Volume 87, ESA'17, Complete Volume}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017},
  URN =		{urn:nbn:de:0030-drops-79096},
  doi =		{10.4230/LIPIcs.ESA.2017},
  annote =	{Keywords: Data Structures, Nonnumerical Algorithms and Problems, Optimization, Discrete Mathematics, Mathematical Software, AlgorithmsProblem Solving, Control Methods, and Search, Computational Geometry and Object Modeling}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.ESA.2017.0

Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers

Authors: Kirk Pruhs and Christian Sohler

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers

Cite as

Kirk Pruhs and Christian Sohler. Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 0:i-0:xx, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{pruhs_et_al:LIPIcs.ESA.2017.0,
  author =	{Pruhs, Kirk and Sohler, Christian},
  title =	{{Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.0},
  URN =		{urn:nbn:de:0030-drops-78147},
  doi =		{10.4230/LIPIcs.ESA.2017.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers}
}

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Invited Talk

DOI: 10.4230/LIPIcs.ESA.2017.1

Sketching for Geometric Problems (Invited Talk)

Authors: David P. Woodruff

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

In this invited talk at the European Symposium on Algorithms (ESA), 2017, I will discuss a tool called sketching, which is a form of data dimensionality reduction, and its applications to several problems in high dimensional geometry. In particular, I will show how to obtain the fastest possible algorithms for fundamental problems such as projection onto a flat, and also study generalizations of projection onto more complicated objects such as the union of flats or subspaces. Some of these problems are just least squares regression problems, with many applications in machine learning, numerical linear algebra, and optimization. I will also discuss low rank approximation, with applications to clustering. Finally I will mention a number of other applications of sketching in machine learning, numerical linear algebra, and optimization.

Cite as

David P. Woodruff. Sketching for Geometric Problems (Invited Talk). In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 1:1-1:5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{woodruff:LIPIcs.ESA.2017.1,
  author =	{Woodruff, David P.},
  title =	{{Sketching for Geometric Problems}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{1:1--1:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.1},
  URN =		{urn:nbn:de:0030-drops-78848},
  doi =		{10.4230/LIPIcs.ESA.2017.1},
  annote =	{Keywords: dimensionality reduction, low rank approximation, projection, regression, sketching}
}

Document

DOI: 10.4230/LIPIcs.ESA.2017.2

Permuting and Batched Geometric Lower Bounds in the I/O Model

Authors: Peyman Afshani and Ingo van Duijn

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

We study permuting and batched orthogonal geometric reporting problems in the External Memory Model (EM), assuming indivisibility of the input records. Our main results are twofold. First, we prove a general simulation result that essentially shows that any permutation algorithm (resp. duplicate removal algorithm) that does alpha*N/B I/Os (resp. to remove a fraction of the existing duplicates) can be simulated with an algorithm that does alpha phases where each phase reads and writes each element once, but using a factor alpha smaller block size. Second, we prove two lower bounds for batched rectangle stabbing and batched orthogonal range reporting queries. Assuming a short cache, we prove very high lower bounds that currently are not possible with the existing techniques under the tall cache assumption.

Cite as

Peyman Afshani and Ingo van Duijn. Permuting and Batched Geometric Lower Bounds in the I/O Model. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 2:1-2:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{afshani_et_al:LIPIcs.ESA.2017.2,
  author =	{Afshani, Peyman and van Duijn, Ingo},
  title =	{{Permuting and Batched Geometric Lower Bounds in the I/O Model}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{2:1--2:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.2},
  URN =		{urn:nbn:de:0030-drops-78695},
  doi =		{10.4230/LIPIcs.ESA.2017.2},
  annote =	{Keywords: I/O Model, Batched Geometric Queries, Lower Bounds, Permuting}
}

Document

DOI: 10.4230/LIPIcs.ESA.2017.3

Independent Range Sampling, Revisited

Authors: Peyman Afshani and Zhewei Wei

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

In the independent range sampling (IRS) problem, given an input set P of n points in R^d, the task is to build a data structure, such that given a range R and an integer t >= 1, it returns t points that are uniformly and independently drawn from P cap R. The samples must satisfy inter-query independence, that is, the samples returned by every query must be independent of the samples returned by all the previous queries. This problem was first tackled by Hu, Qiao and Tao in 2014, who proposed optimal structures for one-dimensional dynamic IRS problem in internal memory and one-dimensional static IRS problem in external memory. In this paper, we study two natural extensions of the independent range sampling problem. In the first extension, we consider the static IRS problem in two and three dimensions in internal memory. We obtain data structures with optimal space-query tradeoffs for 3D halfspace, 3D dominance, and 2D three-sided queries. The second extension considers weighted IRS problem. Each point is associated with a real-valued weight, and given a query range R, a sample is drawn independently such that each point in P cap R is selected with probability proportional to its weight. Walker's alias method is a classic solution to this problem when no query range is specified. We obtain optimal data structure for one dimensional weighted range sampling problem, thereby extending the alias method to allow range queries.

Cite as

Peyman Afshani and Zhewei Wei. Independent Range Sampling, Revisited. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 3:1-3:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{afshani_et_al:LIPIcs.ESA.2017.3,
  author =	{Afshani, Peyman and Wei, Zhewei},
  title =	{{Independent Range Sampling, Revisited}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.3},
  URN =		{urn:nbn:de:0030-drops-78592},
  doi =		{10.4230/LIPIcs.ESA.2017.3},
  annote =	{Keywords: data structures, range searching, range sampling, random sampling}
}

Document

DOI: 10.4230/LIPIcs.ESA.2017.4

Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats

Authors: Pankaj K. Agarwal, Natan Rubin, and Micha Sharir

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

We consider the Approximate Nearest Neighbor (ANN) problem where the input set consists of n k-flats in the Euclidean Rd, for any fixed parameters k<d, and where, for each query point q, we want to return an input flat whose distance from q is at most (1 + epsilon) times the shortest such distance, where epsilon > 0 is another prespecified parameter. We present an algorithm that achieves this task with n^{k+1}(log(n)/epsilon)^O(1) storage and preprocessing (where the constant of proportionality in the big-O notation depends on d), and can answer a query in O(polylog(n)) time (where the power of the logarithm depends on d and k). In particular, we need only near-quadratic storage to answer ANN queries amidst a set of n lines in any fixed-dimensional Euclidean space. As a by-product, our approach also yields an algorithm, with similar performance bounds, for answering exact nearest neighbor queries amidst k-flats with respect to any polyhedral distance function. Our results are more general, in that they also provide a tradeoff between storage and query time.

Cite as

Pankaj K. Agarwal, Natan Rubin, and Micha Sharir. Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 4:1-4:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{agarwal_et_al:LIPIcs.ESA.2017.4,
  author =	{Agarwal, Pankaj K. and Rubin, Natan and Sharir, Micha},
  title =	{{Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.4},
  URN =		{urn:nbn:de:0030-drops-78182},
  doi =		{10.4230/LIPIcs.ESA.2017.4},
  annote =	{Keywords: Approximate nearest neighbor search, k-flats, Polyhedral distance functions, Linear programming queries}
}

Document

DOI: 10.4230/LIPIcs.ESA.2017.5

Output Sensitive Algorithms for Approximate Incidences and Their Applications

Authors: Dror Aiger, Haim Kaplan, and Micha Sharir

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

An epsilon-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most epsilon from each other. Given a set of points and a set of objects, computing the approximate incidences between them is a major step in many database and web-based applications in computer vision and graphics, including robust model fitting, approximate point pattern matching, and estimating the fundamental matrix in epipolar (stereo) geometry. In a typical approximate incidence problem of this sort, we are given a set P of m points in two or three dimensions, a set S of n objects (lines, circles, planes, spheres), and an error parameter epsilon>0, and our goal is to report all pairs (p,s) in P times S that lie at distance at most epsilon from one another. We present efficient output-sensitive approximation algorithms for quite a few cases, including points and lines or circles in the plane, and points and planes, spheres, lines, or circles in three dimensions. Several of these cases arise in the applications mentioned above. Our algorithms report all pairs at distance <= epsilon, but may also report additional pairs, all of which are guaranteed to be at distance at most alphaepsilon, for some constant alpha>1. Our algorithms are based on simple primal and dual grid decompositions and are easy to implement. We note though that (a) the use of duality, which leads to significant improvements in the overhead cost of the algorithms, appears to be novel for this kind of problems; (b) the correct choice of duality in some of these problems is fairly intricate and requires some care; and (c) the correctness and performance analysis of the algorithms (especially in the more advanced versions) is fairly non-trivial. We analyze our algorithms and prove guaranteed upper bounds on their running time and on the "distortion" parameter alpha. We also briefly describe the motivating applications, and show how they can effectively exploit our solutions. The superior theoretical bounds on the performance of our algorithms, and their simplicity, make them indeed ideal tools for these applications. In a series of preliminary experimentations (not included in this abstract), we substantiate this feeling, and show that our algorithms lead in practice to significant improved performance of the aforementioned applications.

Cite as

Dror Aiger, Haim Kaplan, and Micha Sharir. Output Sensitive Algorithms for Approximate Incidences and Their Applications. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 5:1-5:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{aiger_et_al:LIPIcs.ESA.2017.5,
  author =	{Aiger, Dror and Kaplan, Haim and Sharir, Micha},
  title =	{{Output Sensitive Algorithms for Approximate Incidences and Their Applications}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.5},
  URN =		{urn:nbn:de:0030-drops-78224},
  doi =		{10.4230/LIPIcs.ESA.2017.5},
  annote =	{Keywords: Approximate incidences, near-neighbor reporting, duality, grid-based approximation}
}

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