14 Search Results for "P�rez-Lantero, Pablo"


Document
Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization

Authors: Papri Dey, Ravi Kannan, Nick Ryder, and Nikhil Srivastava

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
We study the bit complexity of two related fundamental computational problems in linear algebra and control theory. Our results are: (1) An Õ(n^{ω+3}a+n⁴a²+n^ωlog(1/ε)) time algorithm for finding an ε-approximation to the Jordan Normal form of an integer matrix with a-bit entries, where ω is the exponent of matrix multiplication. (2) An Õ(n⁶d⁶a+n⁴d⁴a²+n³d³log(1/ε)) time algorithm for ε-approximately computing the spectral factorization P(x) = Q^*(x)Q(x) of a given monic n× n rational matrix polynomial of degree 2d with rational a-bit coefficients having a-bit common denominators, which satisfies P(x)⪰0 for all real x. The first algorithm is used as a subroutine in the second one. Despite its being of central importance, polynomial complexity bounds were not previously known for spectral factorization, and for Jordan form the best previous best running time was an unspecified polynomial in n of degree at least twelve [Cai, 1994]. Our algorithms are simple and judiciously combine techniques from numerical and symbolic computation, yielding significant advantages over either approach by itself.

Cite as

Papri Dey, Ravi Kannan, Nick Ryder, and Nikhil Srivastava. Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dey_et_al:LIPIcs.ITCS.2023.42,
  author =	{Dey, Papri and Kannan, Ravi and Ryder, Nick and Srivastava, Nikhil},
  title =	{{Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.42},
  URN =		{urn:nbn:de:0030-drops-175450},
  doi =		{10.4230/LIPIcs.ITCS.2023.42},
  annote =	{Keywords: Symbolic algorithms, numerical algorithms, linear algebra}
}
Document
Invited Talk
Explainability Queries for ML Models and its Connections with Data Management Problems (Invited Talk)

Authors: Pablo Barceló

Published in: LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)


Abstract
In this talk I will present two recent examples of my research on explainability problems over machine learning (ML) models. In rough terms, these explainability problems deal with specific queries one poses over a ML model in order to obtain meaningful justifications for their results. Both of the examples I will present deal with “local” and “post-hoc” explainability queries. Here “local” means that we intend to explain the output of the ML model for a particular input, while “post-hoc” refers to the fact that the explanation is obtained after the model is trained. In the process I will also establish connections with problems studied in data management. This with the intention of suggesting new possibilities for cross-fertilization between the area and ML. The first example I will present refers to computing explanations with scores based on Shapley values, in particular with the recently proposed, and already influential, SHAP-score. This score provides a measure of how different features in the input contribute to the output of the ML model. We provide a detailed analysis of the complexity of this problem for different classes of Boolean circuits. In particular, we show that the problem of computing SHAP-scores is tractable as long as the circuit is deterministic and decomposable, but becomes computationally hard if any of these restrictions is lifted. The tractability part of this result provides a generalization of a recent result stating that, for Boolean hierarchical conjunctive queries, the Shapley-value of the contribution of a tuple in the database to the final result can be computed in polynomial time. The second example I will present refers to the comparison of different ML models in terms of important families of (local and post-hoc) explainability queries. For the models, I will consider multi-layer perceptrons and binary decision diagrams. The main object of study will be the computational complexity of the aforementioned queries over such models. The obtained results will show an interesting theoretical counterpart to wisdom’s claims on interpretability. This work also suggests the need for developing query languages that support the process of retrieving explanations from ML models, and also for obtaining general tractability results for such languages over specific classes of models.

Cite as

Pablo Barceló. Explainability Queries for ML Models and its Connections with Data Management Problems (Invited Talk). In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{barcelo:LIPIcs.ICDT.2021.1,
  author =	{Barcel\'{o}, Pablo},
  title =	{{Explainability Queries for ML Models and its Connections with Data Management Problems}},
  booktitle =	{24th International Conference on Database Theory (ICDT 2021)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-179-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{186},
  editor =	{Yi, Ke and Wei, Zhewei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.1},
  URN =		{urn:nbn:de:0030-drops-137091},
  doi =		{10.4230/LIPIcs.ICDT.2021.1},
  annote =	{Keywords: ML models, Explainability, Shapley values, decision trees, OBDDs, deterministic and decomposable Boolean circuits}
}
Document
On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra

Authors: Pablo Barceló, Nelson Higuera, Jorge Pérez, and Bernardo Subercaseaux

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)


Abstract
We study the expressive power of the Lara language - a recently proposed unified model for expressing relational and linear algebra operations - both in terms of traditional database query languages and some analytic tasks often performed in machine learning pipelines. We start by showing Lara to be expressive complete with respect to first-order logic with aggregation. Since Lara is parameterized by a set of user-defined functions which allow to transform values in tables, the exact expressive power of the language depends on how these functions are defined. We distinguish two main cases depending on the level of genericity queries are enforced to satisfy. Under strong genericity assumptions the language cannot express matrix convolution, a very important operation in current machine learning operations. This language is also local, and thus cannot express operations such as matrix inverse that exhibit a recursive behavior. For expressing convolution, one can relax the genericity requirement by adding an underlying linear order on the domain. This, however, destroys locality and turns the expressive power of the language much more difficult to understand. In particular, although under complexity assumptions the resulting language can still not express matrix inverse, a proof of this fact without such assumptions seems challenging to obtain.

Cite as

Pablo Barceló, Nelson Higuera, Jorge Pérez, and Bernardo Subercaseaux. On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{barcelo_et_al:LIPIcs.ICDT.2020.6,
  author =	{Barcel\'{o}, Pablo and Higuera, Nelson and P\'{e}rez, Jorge and Subercaseaux, Bernardo},
  title =	{{On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.6},
  URN =		{urn:nbn:de:0030-drops-119305},
  doi =		{10.4230/LIPIcs.ICDT.2020.6},
  annote =	{Keywords: languages for linear and relational algebra, expressive power, first order logic with aggregation, matrix convolution, matrix inverse, query genericity, locality of queries, safety}
}
Document
Simplifying Inductive Schemes in Temporal Logic

Authors: Pablo Cordero, Inmaculada Fortes, Inmaculada P. de Guzmán, and Sixto Sánchez

Published in: LIPIcs, Volume 147, 26th International Symposium on Temporal Representation and Reasoning (TIME 2019)


Abstract
In propositional temporal logic, the combination of the connectives "tomorrow" and "always in the future" require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula.

Cite as

Pablo Cordero, Inmaculada Fortes, Inmaculada P. de Guzmán, and Sixto Sánchez. Simplifying Inductive Schemes in Temporal Logic. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 19:1-19:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{cordero_et_al:LIPIcs.TIME.2019.19,
  author =	{Cordero, Pablo and Fortes, Inmaculada and de Guzm\'{a}n, Inmaculada P. and S\'{a}nchez, Sixto},
  title =	{{Simplifying Inductive Schemes in Temporal Logic}},
  booktitle =	{26th International Symposium on Temporal Representation and Reasoning (TIME 2019)},
  pages =	{19:1--19:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-127-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{147},
  editor =	{Gamper, Johann and Pinchinat, Sophie and Sciavicco, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2019.19},
  URN =		{urn:nbn:de:0030-drops-113773},
  doi =		{10.4230/LIPIcs.TIME.2019.19},
  annote =	{Keywords: Linear Temporal Logic, Inductive Schemes, Loop-check}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Boundedness of Conjunctive Regular Path Queries (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Pablo Barceló, Diego Figueira, and Miguel Romero

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


Abstract
We study the boundedness problem for unions of conjunctive regular path queries with inverses (UC2RPQs). This is the problem of, given a UC2RPQ, checking whether it is equivalent to a union of conjunctive queries (UCQ). We show the problem to be ExpSpace-complete, thus coinciding with the complexity of containment for UC2RPQs. As a corollary, when a UC2RPQ is bounded, it is equivalent to a UCQ of at most triple-exponential size, and in fact we show that this bound is optimal. We also study better behaved classes of UC2RPQs, namely acyclic UC2RPQs of bounded thickness, and strongly connected UCRPQs, whose boundedness problem is, respectively, PSpace-complete and Pi_2^P-complete. Most upper bounds exploit results on limitedness for distance automata, in particular extending the model with alternation and two-wayness, which may be of independent interest.

Cite as

Pablo Barceló, Diego Figueira, and Miguel Romero. Boundedness of Conjunctive Regular Path Queries (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 104:1-104:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{barcelo_et_al:LIPIcs.ICALP.2019.104,
  author =	{Barcel\'{o}, Pablo and Figueira, Diego and Romero, Miguel},
  title =	{{Boundedness of Conjunctive Regular Path Queries}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{104:1--104:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.104},
  URN =		{urn:nbn:de:0030-drops-106803},
  doi =		{10.4230/LIPIcs.ICALP.2019.104},
  annote =	{Keywords: regular path queries, boundedness, limitedness, distance automata}
}
Document
Dichotomic Selection on Words: A Probabilistic Analysis

Authors: Ali Akhavi, Julien Clément, Dimitri Darthenay, Loïck Lhote, and Brigitte Vallée

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)


Abstract
The paper studies the behaviour of selection algorithms that are based on dichotomy principles. On the entry formed by an ordered list L and a searched element x not in L, they return the interval of the list L the element x belongs to. We focus here on the case of words, where dichotomy principles lead to a selection algorithm designed by Crochemore, Hancart and Lecroq, which appears to be "quasi-optimal". We perform a probabilistic analysis of this algorithm that exhibits its quasi-optimality on average.

Cite as

Ali Akhavi, Julien Clément, Dimitri Darthenay, Loïck Lhote, and Brigitte Vallée. Dichotomic Selection on Words: A Probabilistic Analysis. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{akhavi_et_al:LIPIcs.CPM.2019.19,
  author =	{Akhavi, Ali and Cl\'{e}ment, Julien and Darthenay, Dimitri and Lhote, Lo\"{i}ck and Vall\'{e}e, Brigitte},
  title =	{{Dichotomic Selection on Words: A Probabilistic Analysis}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.19},
  URN =		{urn:nbn:de:0030-drops-104903},
  doi =		{10.4230/LIPIcs.CPM.2019.19},
  annote =	{Keywords: dichotomic selection, text algorithms, analysis of algorithms, average case analysis of algorithms, trie, suffix array, lcp-array, information theory, numeration process, sources, entropy, coincidence, analytic combinatorics, depoissonization techniques}
}
Document
Invited Talk
Learning Models over Relational Databases (Invited Talk)

Authors: Dan Olteanu

Published in: LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)


Abstract
In this talk, I will make the case for a first-principles approach to machine learning over relational databases that exploits recent development in database systems and theory. The input to learning classification and regression models is defined by feature extraction queries over relational databases. The mainstream approach to learning over relational data is to materialize the training dataset, export it out of the database, and then learn over it using statistical software packages. These three steps are expensive and unnecessary. Instead, one can cast the machine learning problem as a database problem by decomposing the learning task into a batch of aggregates over the feature extraction query and by computing this batch over the input database. The performance of this database-centric approach benefits tremendously from structural properties of the relational data and of the feature extraction query; such properties may be algebraic (semi-ring), combinatorial (hypertree width), or statistical (sampling). It also benefits from database systems techniques such as factorized query evaluation and query compilation. For a variety of models, including factorization machines, decision trees, and support vector machines, this approach may come with lower computational complexity than the materialization of the training dataset used by the mainstream approach. Recent results show that this translates to several orders-of-magnitude speed-up over state-of-the-art systems such as TensorFlow, R, Scikit-learn, and mlpack. While these initial results are promising, there is much more awaiting to be discovered.

Cite as

Dan Olteanu. Learning Models over Relational Databases (Invited Talk). In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{olteanu:LIPIcs.ICDT.2019.1,
  author =	{Olteanu, Dan},
  title =	{{Learning Models over Relational Databases}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Barcelo, Pablo and Calautti, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.1},
  URN =		{urn:nbn:de:0030-drops-103034},
  doi =		{10.4230/LIPIcs.ICDT.2019.1},
  annote =	{Keywords: In-database analytics, Data complexity, Feature extraction queries, Database dependencies, Model reparameterization}
}
Document
Invited Talk
The Power of Relational Learning (Invited Talk)

Authors: Lise Getoor

Published in: LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)


Abstract
We live in a richly interconnected world and, not surprisingly, we generate richly interconnected data. From smart cities to social media to financial networks to biological networks, data is relational. While database theory is built on strong relational foundations, the same is not true for machine learning. The majority of machine learning methods flatten data into a single table before performing any processing. Further, database theory is also built on a bedrock of declarative representations. The same is not true for machine learning, in particular deep learning, which results in black-box, uninterpretable and unexplainable models. In this talk, I will introduce the field of statistical relational learning, an alternative machine learning approach based on declarative relational representations paired with probabilistic models. I’ll describe our work on probabilistic soft logic, a probabilistic programming language that is ideally suited to richly connected, noisy data. Our recent results show that by building on state-of-the-art optimization methods in a distributed implementation, we can solve very large relational learning problems orders of magnitude faster than existing approaches.

Cite as

Lise Getoor. The Power of Relational Learning (Invited Talk). In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{getoor:LIPIcs.ICDT.2019.2,
  author =	{Getoor, Lise},
  title =	{{The Power of Relational Learning}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Barcelo, Pablo and Calautti, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.2},
  URN =		{urn:nbn:de:0030-drops-103048},
  doi =		{10.4230/LIPIcs.ICDT.2019.2},
  annote =	{Keywords: Machine learning, Probabilistic soft logic, Relational model}
}
Document
Consistent Query Answering for Primary Keys in Logspace

Authors: Paraschos Koutris and Jef Wijsen

Published in: LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)


Abstract
We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In [Koutris and Wijsen, ACM TODS, 2017], the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this paper, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog (with some aggregation operator) or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.

Cite as

Paraschos Koutris and Jef Wijsen. Consistent Query Answering for Primary Keys in Logspace. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{koutris_et_al:LIPIcs.ICDT.2019.23,
  author =	{Koutris, Paraschos and Wijsen, Jef},
  title =	{{Consistent Query Answering for Primary Keys in Logspace}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Barcelo, Pablo and Calautti, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.23},
  URN =		{urn:nbn:de:0030-drops-103252},
  doi =		{10.4230/LIPIcs.ICDT.2019.23},
  annote =	{Keywords: conjunctive queries, consistent query answering, Datalog, primary keys}
}
Document
On Guillotine Cutting Sequences

Authors: Fidaa Abed, Parinya Chalermsook, José Correa, Andreas Karrenbauer, Pablo Pérez-Lantero, José A. Soto, and Andreas Wiese

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
Imagine a wooden plate with a set of non-overlapping geometric objects painted on it. How many of them can a carpenter cut out using a panel saw making guillotine cuts, i.e., only moving forward through the material along a straight line until it is split into two pieces? Already fifteen years ago, Pach and Tardos investigated whether one can always cut out a constant fraction if all objects are axis-parallel rectangles. However, even for the case of axis-parallel squares this question is still open. In this paper, we answer the latter affirmatively. Our result is constructive and holds even in a more general setting where the squares have weights and the goal is to save as much weight as possible. We further show that when solving the more general question for rectangles affirmatively with only axis-parallel cuts, this would yield a combinatorial O(1)-approximation algorithm for the Maximum Independent Set of Rectangles problem, and would thus solve a long-standing open problem. In practical applications, like the mentioned carpentry and many other settings, we can usually place the items freely that we want to cut out, which gives rise to the two-dimensional guillotine knapsack problem: Given a collection of axis-parallel rectangles without presumed coordinates, our goal is to place as many of them as possible in a square-shaped knapsack respecting the constraint that the placed objects can be separated by a sequence of guillotine cuts. Our main result for this problem is a quasi-PTAS, assuming the input data to be quasi-polynomially bounded integers. This factor matches the best known (quasi-polynomial time) result for (non-guillotine) two-dimensional knapsack.

Cite as

Fidaa Abed, Parinya Chalermsook, José Correa, Andreas Karrenbauer, Pablo Pérez-Lantero, José A. Soto, and Andreas Wiese. On Guillotine Cutting Sequences. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{abed_et_al:LIPIcs.APPROX-RANDOM.2015.1,
  author =	{Abed, Fidaa and Chalermsook, Parinya and Correa, Jos\'{e} and Karrenbauer, Andreas and P\'{e}rez-Lantero, Pablo and Soto, Jos\'{e} A. and Wiese, Andreas},
  title =	{{On Guillotine Cutting Sequences}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{1--19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.1},
  URN =		{urn:nbn:de:0030-drops-52917},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.1},
  annote =	{Keywords: Guillotine cuts, Rectangles, Squares, Independent Sets, Packing}
}
Document
On the Data Complexity of Consistent Query Answering over Graph Databases

Authors: Pablo Barceló and Gaëlle Fontaine

Published in: LIPIcs, Volume 31, 18th International Conference on Database Theory (ICDT 2015)


Abstract
Areas in which graph databases are applied - such as the semantic web, social networks and scientific databases - are prone to inconsistency, mainly due to interoperability issues. This raises the need for understanding query answering over inconsistent graph databases in a framework that is simple yet general enough to accommodate many of its applications. We follow the well-known approach of consistent query answering (CQA), and study the data complexity of CQA over graph databases for regular path queries (RPQs) and regular path constraints (RPCs), which are frequently used. We concentrate on subset, superset and symmetric difference repairs. Without further restrictions, CQA is undecidable for the semantics based on superset and symmetric difference repairs, and Pi_2^P-complete for subset repairs. However, we provide several tractable restrictions on both RPCs and the structure of graph databases that lead to decidability, and even tractability of CQA. We also compare our results with those obtained for CQA in the context of relational databases.

Cite as

Pablo Barceló and Gaëlle Fontaine. On the Data Complexity of Consistent Query Answering over Graph Databases. In 18th International Conference on Database Theory (ICDT 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 31, pp. 380-397, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{barcelo_et_al:LIPIcs.ICDT.2015.380,
  author =	{Barcel\'{o}, Pablo and Fontaine, Ga\"{e}lle},
  title =	{{On the Data Complexity of Consistent Query Answering over Graph Databases}},
  booktitle =	{18th International Conference on Database Theory (ICDT 2015)},
  pages =	{380--397},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-79-8},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{31},
  editor =	{Arenas, Marcelo and Ugarte, Mart{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2015.380},
  URN =		{urn:nbn:de:0030-drops-49962},
  doi =		{10.4230/LIPIcs.ICDT.2015.380},
  annote =	{Keywords: graph databases, regular path queries, consistent query answering, description logics, rewrite systems}
}
Document
Regulated MAS: Social Perspective

Authors: Pablo Noriega, Amit K. Chopra, Nicoletta Fornara, Henrique Lopes Cardoso, and Munindar P. Singh

Published in: Dagstuhl Follow-Ups, Volume 4, Normative Multi-Agent Systems (2013)


Abstract
This chapter addresses the problem of building normative multiagent systems in terms of regulatory mechanisms. It describes a static conceptual model through which one can specify normative multiagent systems along with a dynamic model to capture their operation and evolution. The chapter proposes a typology of applications and presents some open problems. In the last section, the authors express their individual views on these matters.

Cite as

Pablo Noriega, Amit K. Chopra, Nicoletta Fornara, Henrique Lopes Cardoso, and Munindar P. Singh. Regulated MAS: Social Perspective. In Normative Multi-Agent Systems. Dagstuhl Follow-Ups, Volume 4, pp. 93-133, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InCollection{noriega_et_al:DFU.Vol4.12111.93,
  author =	{Noriega, Pablo and Chopra, Amit K. and Fornara, Nicoletta and Lopes Cardoso, Henrique and Singh, Munindar P.},
  title =	{{Regulated MAS: Social Perspective}},
  booktitle =	{Normative Multi-Agent Systems},
  pages =	{93--133},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-51-4},
  ISSN =	{1868-8977},
  year =	{2013},
  volume =	{4},
  editor =	{Andrighetto, Giulia and Governatori, Guido and Noriega, Pablo and van der Torre, Leendert W. N.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DFU.Vol4.12111.93},
  URN =		{urn:nbn:de:0030-drops-40017},
  doi =		{10.4230/DFU.Vol4.12111.93},
  annote =	{Keywords: NormMAS, Norms, Open Interaction}
}
Document
The Uses of Norms

Authors: Munindar P. Singh, Matthew Arrott, Tina Balke, Amit K. Chopra, Rob Christiaanse, Stephen Cranefield, Frank Dignum, Davide Eynard, Emilia Farcas, Nicoletta Fornara, Fabien Gandon, Guido Governatori, Hoa Khanh Dam, Joris Hulstijn, Ingolf Krueger, Ho-Pun Lam, Michael Meisinger, Pablo Noriega, Bastin Tony Roy Savarimuthu, Kartik Tadanki, Harko Verhagen, and Serena Villata

Published in: Dagstuhl Follow-Ups, Volume 4, Normative Multi-Agent Systems (2013)


Abstract
This chapter presents a variety of applications of norms. These applications include governance in sociotechnical systems, data licensing and data collection, understanding software development teams, requirements engineering, assurance, natural resource allocation, wireless grids, autonomous vehicles, serious games, and virtual worlds.

Cite as

Munindar P. Singh, Matthew Arrott, Tina Balke, Amit K. Chopra, Rob Christiaanse, Stephen Cranefield, Frank Dignum, Davide Eynard, Emilia Farcas, Nicoletta Fornara, Fabien Gandon, Guido Governatori, Hoa Khanh Dam, Joris Hulstijn, Ingolf Krueger, Ho-Pun Lam, Michael Meisinger, Pablo Noriega, Bastin Tony Roy Savarimuthu, Kartik Tadanki, Harko Verhagen, and Serena Villata. The Uses of Norms. In Normative Multi-Agent Systems. Dagstuhl Follow-Ups, Volume 4, pp. 191-229, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InCollection{singh_et_al:DFU.Vol4.12111.191,
  author =	{Singh, Munindar P. and Arrott, Matthew and Balke, Tina and Chopra, Amit K. and Christiaanse, Rob and Cranefield, Stephen and Dignum, Frank and Eynard, Davide and Farcas, Emilia and Fornara, Nicoletta and Gandon, Fabien and Governatori, Guido and Khanh Dam, Hoa and Hulstijn, Joris and Krueger, Ingolf and Lam, Ho-Pun and Meisinger, Michael and Noriega, Pablo and Savarimuthu, Bastin Tony Roy and Tadanki, Kartik and Verhagen, Harko and Villata, Serena},
  title =	{{The Uses of Norms}},
  booktitle =	{Normative Multi-Agent Systems},
  pages =	{191--229},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-51-4},
  ISSN =	{1868-8977},
  year =	{2013},
  volume =	{4},
  editor =	{Andrighetto, Giulia and Governatori, Guido and Noriega, Pablo and van der Torre, Leendert W. N.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DFU.Vol4.12111.191},
  URN =		{urn:nbn:de:0030-drops-40047},
  doi =		{10.4230/DFU.Vol4.12111.191},
  annote =	{Keywords: Norms, MAS, Governance, Requirements engineering}
}
Document
FSL – Fibred Security Language

Authors: Valerio Genovese, Dov M. Gabbay, Guido Boella, and Leendert van der Torre

Published in: Dagstuhl Seminar Proceedings, Volume 9121, Normative Multi-Agent Systems (2009)


Abstract
We develop a fibred security language capable to express statements of the form begin{center} ${x }varphi (x) says psi$ end{center} where ${x}varphi (x)$ is the set of all $x$ that satisfy $varphi$ and $psi$ is any formula. $varphi$ and $psi$ may share several free variables. For example, we can express the following: "A member $m$ of the Program Committee can not accept a paper $P_1$ in which one of its authors says that he has published a paper with him after 2007" begin{center} $ eg({m} [PC(m) wedge {y}author\_of(y,P_1) extbf{ says } exists p(paper(p) wedge author\_of(m,p) wedge author\_of(y,p) wedge year(p) geq 2007)] extbf{ says } accept(P_1))$ end{center}

Cite as

Valerio Genovese, Dov M. Gabbay, Guido Boella, and Leendert van der Torre. FSL – Fibred Security Language. In Normative Multi-Agent Systems. Dagstuhl Seminar Proceedings, Volume 9121, pp. 1-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{genovese_et_al:DagSemProc.09121.16,
  author =	{Genovese, Valerio and Gabbay, Dov M. and Boella, Guido and van der Torre, Leendert},
  title =	{{FSL – Fibred Security Language}},
  booktitle =	{Normative Multi-Agent Systems},
  pages =	{1--29},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9121},
  editor =	{Guido Boella and Pablo Noriega and Gabriella Pigozzi and Harko Verhagen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09121.16},
  URN =		{urn:nbn:de:0030-drops-19083},
  doi =		{10.4230/DagSemProc.09121.16},
  annote =	{Keywords: Access Control, Trust Management, Fibring Logics}
}
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