24 Search Results for "M�der, Patrick"

Document
DOI: 10.4230/LIPIcs.IPEC.2023.14
Computing Complexity Measures of Degenerate Graphs

Authors: Pål Grønås Drange, Patrick Greaves, Irene Muzi, and Felix Reidl

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
We show that the VC-dimension of a graph can be computed in time n^{⌈log d+1⌉} d^{O(d)}, where d is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that see a specific subset of vertices inside of a (small) query set. The construction of this data structure takes time O(d2^dn), afterwards queries can be computed efficiently using fast Möbius inversion. This data structure turns out to be useful for a range of tasks, especially for finding bipartite patterns in degenerate graphs, and we outline an efficient algorithm for counting the number of times specific patterns occur in a graph. The largest factor in the running time of this algorithm is O(n^c), where c is a parameter of the pattern we call its left covering number. Concrete applications of this algorithm include counting the number of (non-induced) bicliques in linear time, the number of co-matchings in quadratic time, as well as a constant-factor approximation of the ladder index in linear time. Finally, we supplement our theoretical results with several implementations and run experiments on more than 200 real-world datasets - the largest of which has 8 million edges - where we obtain interesting insights into the VC-dimension of real-world networks.
Cite as

Pål Grønås Drange, Patrick Greaves, Irene Muzi, and Felix Reidl. Computing Complexity Measures of Degenerate Graphs. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{drange_et_al:LIPIcs.IPEC.2023.14,
  author =	{Drange, P\r{a}l Gr{\o}n\r{a}s and Greaves, Patrick and Muzi, Irene and Reidl, Felix},
  title =	{{Computing Complexity Measures of Degenerate Graphs}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.14},
  URN =		{urn:nbn:de:0030-drops-194333},
  doi =		{10.4230/LIPIcs.IPEC.2023.14},
  annote =	{Keywords: vc-dimension, datastructure, degeneracy, enumerating}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.15
An FPT Algorithm for Splitting a Necklace Among Two Thieves

Authors: Michaela Borzechowski, Patrick Schnider, and Simon Weber

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
It is well-known that the 2-Thief-Necklace-Splitting problem reduces to the discrete Ham Sandwich problem. In fact, this reduction was crucial in the proof of the PPA-completeness of the Ham Sandwich problem [Filos-Ratsikas and Goldberg, STOC'19]. Recently, a variant of the Ham Sandwich problem called α-Ham Sandwich has been studied, in which the point sets are guaranteed to be well-separated [Steiger and Zhao, DCG'10]. The complexity of this search problem remains unknown, but it is known to lie in the complexity class UEOPL [Chiu, Choudhary and Mulzer, ICALP'20]. We define the analogue of this well-separation condition in the necklace splitting problem - a necklace is n-separable, if every subset A of the n types of jewels can be separated from the types [n]⧵A by at most n separator points. Since this version of necklace splitting reduces to α-Ham Sandwich in a solution-preserving way it follows that instances of this version always have unique solutions. We furthermore provide two FPT algorithms: The first FPT algorithm solves 2-Thief-Necklace-Splitting on (n-1+𝓁)-separable necklaces with n types of jewels and m total jewels in time 2^O(𝓁log𝓁) + O(m²). In particular, this shows that 2-Thief-Necklace-Splitting is polynomial-time solvable on n-separable necklaces. Thus, attempts to show hardness of α-Ham Sandwich through reduction from the 2-Thief-Necklace-Splitting problem cannot work. The second FPT algorithm tests (n-1+𝓁)-separability of a given necklace with n types of jewels in time 2^O(𝓁²) ⋅ n⁴. In particular, n-separability can thus be tested in polynomial time, even though testing well-separation of point sets is co-NP-complete [Bergold et al., SWAT'22].
Cite as

Michaela Borzechowski, Patrick Schnider, and Simon Weber. An FPT Algorithm for Splitting a Necklace Among Two Thieves. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{borzechowski_et_al:LIPIcs.ISAAC.2023.15,
  author =	{Borzechowski, Michaela and Schnider, Patrick and Weber, Simon},
  title =	{{An FPT Algorithm for Splitting a Necklace Among Two Thieves}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{15:1--15:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.15},
  URN =		{urn:nbn:de:0030-drops-193178},
  doi =		{10.4230/LIPIcs.ISAAC.2023.15},
  annote =	{Keywords: Necklace splitting, n-separability, well-separation, ham sandwich, FPT}
}
Document
DOI: 10.4230/LIPIcs.TQC.2023.12
Efficient Tomography of Non-Interacting-Fermion States

Authors: Scott Aaronson and Sabee Grewal

Published in: LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)

Abstract
We give an efficient algorithm that learns a non-interacting-fermion state, given copies of the state. For a system of n non-interacting fermions and m modes, we show that O(m³ n² log(1/δ) / ε⁴) copies of the input state and O(m⁴ n² log(1/δ)/ ε⁴) time are sufficient to learn the state to trace distance at most ε with probability at least 1 - δ. Our algorithm empirically estimates one-mode correlations in O(m) different measurement bases and uses them to reconstruct a succinct description of the entire state efficiently.
Cite as

Scott Aaronson and Sabee Grewal. Efficient Tomography of Non-Interacting-Fermion States. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{aaronson_et_al:LIPIcs.TQC.2023.12,
  author =	{Aaronson, Scott and Grewal, Sabee},
  title =	{{Efficient Tomography of Non-Interacting-Fermion States}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.12},
  URN =		{urn:nbn:de:0030-drops-183222},
  doi =		{10.4230/LIPIcs.TQC.2023.12},
  annote =	{Keywords: free-fermions, Gaussian fermions, non-interacting fermions, quantum state tomography, efficient tomography}
}
Document
DOI: 10.4230/OASIcs.EVCS.2023.5
Spoofax at Oracle: Domain-Specific Language Engineering for Large-Scale Graph Analytics

Authors: Houda Boukham, Guido Wachsmuth, Toine Hartman, Hamza Boucherit, Oskar van Rest, Hassan Chafi, Sungpack Hong, Martijn Dwars, Arnaud Delamare, and Dalila Chiadmi

Published in: OASIcs, Volume 109, Eelco Visser Commemorative Symposium (EVCS 2023)

Abstract
For the last decade, teams at Oracle relied on the Spoofax language workbench to develop a family of domain-specific languages for graph analytics in research projects and in product development. In this paper, we analyze the requirements for integrating language processors into large-scale graph analytics toolkits and for the development of these language processors as part of a larger product development process. We discuss how Spoofax helps to meet these requirements and point out the need for future improvements.
Cite as

Houda Boukham, Guido Wachsmuth, Toine Hartman, Hamza Boucherit, Oskar van Rest, Hassan Chafi, Sungpack Hong, Martijn Dwars, Arnaud Delamare, and Dalila Chiadmi. Spoofax at Oracle: Domain-Specific Language Engineering for Large-Scale Graph Analytics. In Eelco Visser Commemorative Symposium (EVCS 2023). Open Access Series in Informatics (OASIcs), Volume 109, pp. 5:1-5:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{boukham_et_al:OASIcs.EVCS.2023.5,
  author =	{Boukham, Houda and Wachsmuth, Guido and Hartman, Toine and Boucherit, Hamza and van Rest, Oskar and Chafi, Hassan and Hong, Sungpack and Dwars, Martijn and Delamare, Arnaud and Chiadmi, Dalila},
  title =	{{Spoofax at Oracle: Domain-Specific Language Engineering for Large-Scale Graph Analytics}},
  booktitle =	{Eelco Visser Commemorative Symposium (EVCS 2023)},
  pages =	{5:1--5:8},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-267-9},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{109},
  editor =	{L\"{a}mmel, Ralf and Mosses, Peter D. and Steimann, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.EVCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-177756},
  doi =		{10.4230/OASIcs.EVCS.2023.5},
  annote =	{Keywords: language workbench, domain-specific language}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.23
Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean

Authors: Yury Kudryashov

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
I formalize a version of the divergence theorem for a function on a rectangular box that does not assume regularity of individual partial derivatives, only Fréchet differentiability of the vector field and integrability of its divergence. Then I use this theorem to prove the Cauchy-Goursat theorem (for some simple domains) and bootstrap complex analysis in the Lean mathematical library. The main tool is the GP-integral, a version of the Henstock-Kurzweil integral introduced by J. Mawhin in 1981. The divergence theorem for this integral does not require integrability of the divergence.
Cite as

Yury Kudryashov. Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kudryashov:LIPIcs.ITP.2022.23,
  author =	{Kudryashov, Yury},
  title =	{{Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.23},
  URN =		{urn:nbn:de:0030-drops-167326},
  doi =		{10.4230/LIPIcs.ITP.2022.23},
  annote =	{Keywords: divergence theorem, Green’s theorem, Gauge integral, Cauchy integral formula, Cauchy-Goursat theorem, complex analysis}
}
Document
DOI: 10.4230/OASIcs.iPMVM.2020.10
Is Smaller Always Better? - Evaluating Video Compression Techniques for Simulation Ensembles

Authors: Patrick Ruediger, Christoph Garth, Hans Hagen, and Heike Leitte

Published in: OASIcs, Volume 89, 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)

Abstract
We provide an evaluation of the applicability of video compression techniques for compressing visualization image databases that are often used for in situ visualization. Considering relevant practical implementation aspects, we identify relevant compression parameters, and evaluate video compression for several test cases, involving several data sets and visualization methods; we use three different video codecs. To quantify the benefits and drawbacks of video compression, we employ metrics for image quality, compression rate, and performance. The experiments discussed provide insight into good choices of parameter values, working well in the considered cases.
Cite as

Patrick Ruediger, Christoph Garth, Hans Hagen, and Heike Leitte. Is Smaller Always Better? - Evaluating Video Compression Techniques for Simulation Ensembles. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ruediger_et_al:OASIcs.iPMVM.2020.10,
  author =	{Ruediger, Patrick and Garth, Christoph and Hagen, Hans and Leitte, Heike},
  title =	{{Is Smaller Always Better? - Evaluating Video Compression Techniques for Simulation Ensembles}},
  booktitle =	{2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)},
  pages =	{10:1--10:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-183-2},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{89},
  editor =	{Garth, Christoph and Aurich, Jan C. and Linke, Barbara and M\"{u}ller, Ralf and Ravani, Bahram and Weber, Gunther H. and Kirsch, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.iPMVM.2020.10},
  URN =		{urn:nbn:de:0030-drops-137591},
  doi =		{10.4230/OASIcs.iPMVM.2020.10},
  annote =	{Keywords: Image Database, CinemaDB, Video Compression, Evaluation, Benchmark, In-situ}
}
Document
DOI: 10.4230/LIPIcs.CCC.2020.7
Quantum Lower Bounds for Approximate Counting via Laurent Polynomials

Authors: Scott Aaronson, Robin Kothari, William Kretschmer, and Justin Thaler

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

Abstract
We study quantum algorithms that are given access to trusted and untrusted quantum witnesses. We establish strong limitations of such algorithms, via new techniques based on Laurent polynomials (i.e., polynomials with positive and negative integer exponents). Specifically, we resolve the complexity of approximate counting, the problem of multiplicatively estimating the size of a nonempty set S ⊆ [N], in two natural generalizations of quantum query complexity. Our first result holds in the standard Quantum Merlin - Arthur (QMA) setting, in which a quantum algorithm receives an untrusted quantum witness. We show that, if the algorithm makes T quantum queries to S, and also receives an (untrusted) m-qubit quantum witness, then either m = Ω(|S|) or T = Ω(√{N/|S|}). This is optimal, matching the straightforward protocols where the witness is either empty, or specifies all the elements of S. As a corollary, this resolves the open problem of giving an oracle separation between SBP, the complexity class that captures approximate counting, and QMA. In our second result, we ask what if, in addition to a membership oracle for S, a quantum algorithm is also given "QSamples" - i.e., copies of the state |S⟩ = 1/√|S| ∑_{i ∈ S} |i⟩ - or even access to a unitary transformation that enables QSampling? We show that, even then, the algorithm needs either Θ(√{N/|S|}) queries or else Θ(min{|S|^{1/3},√{N/|S|}}) QSamples or accesses to the unitary. Our lower bounds in both settings make essential use of Laurent polynomials, but in different ways.
Cite as

Scott Aaronson, Robin Kothari, William Kretschmer, and Justin Thaler. Quantum Lower Bounds for Approximate Counting via Laurent Polynomials. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 7:1-7:47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aaronson_et_al:LIPIcs.CCC.2020.7,
  author =	{Aaronson, Scott and Kothari, Robin and Kretschmer, William and Thaler, Justin},
  title =	{{Quantum Lower Bounds for Approximate Counting via Laurent Polynomials}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{7:1--7:47},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.7},
  URN =		{urn:nbn:de:0030-drops-125593},
  doi =		{10.4230/LIPIcs.CCC.2020.7},
  annote =	{Keywords: Approximate counting, Laurent polynomials, QSampling, query complexity}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.23
Trajectory Visibility

Authors: Patrick Eades, Ivor van der Hoog, Maarten Löffler, and Frank Staals

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
We study the problem of testing whether there exists a time at which two entities moving along different piece-wise linear trajectories among polygonal obstacles are mutually visible. We study several variants, depending on whether or not the obstacles form a simple polygon, trajectories may intersect the polygon edges, and both or only one of the entities are moving. For constant complexity trajectories contained in a simple polygon with n vertices, we provide an 𝒪(n) time algorithm to test if there is a time at which the entities can see each other. If the polygon contains holes, we present an 𝒪(n log n) algorithm. We show that this is tight. We then consider storing the obstacles in a data structure, such that queries consisting of two line segments can be efficiently answered. We show that for all variants it is possible to answer queries in sublinear time using polynomial space and preprocessing time. As a critical intermediate step, we provide an efficient solution to a problem of independent interest: preprocess a convex polygon such that we can efficiently test intersection with a quadratic curve segment. If the obstacles form a simple polygon, this allows us to answer visibility queries in 𝒪(n³/4log³ n) time using 𝒪(nlog⁵ n) space. For more general obstacles the query time is 𝒪(log^k n), for a constant but large value k, using 𝒪(n^{3k}) space. We provide more efficient solutions when one of the entities remains stationary.
Cite as

Patrick Eades, Ivor van der Hoog, Maarten Löffler, and Frank Staals. Trajectory Visibility. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{eades_et_al:LIPIcs.SWAT.2020.23,
  author =	{Eades, Patrick and van der Hoog, Ivor and L\"{o}ffler, Maarten and Staals, Frank},
  title =	{{Trajectory Visibility}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.23},
  URN =		{urn:nbn:de:0030-drops-122701},
  doi =		{10.4230/LIPIcs.SWAT.2020.23},
  annote =	{Keywords: trajectories, visibility, data structures, semi-algebraic range searching}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2019.11
Maximizing the Number of Rides Served for Dial-a-Ride

Authors: Barbara M. Anthony, Ricky Birnbaum, Sara Boyd, Ananya Christman, Christine Chung, Patrick Davis, Jigar Dhimar, and David Yuen

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)

Abstract
We study a variation of offline Dial-a-Ride, where each request has not only a source and destination, but also a revenue that is earned for serving the request. We investigate this problem for the uniform metric space with uniform revenues. While we present a study on a simplified setting of the problem that has limited practical applications, this work provides the theoretical foundation for analyzing the more general forms of the problem. Since revenues are uniform the problem is equivalent to maximizing the number of served requests. We show that the problem is NP-hard and present a 2/3 approximation algorithm. We also show that a natural generalization of this algorithm has an approximation ratio at most 7/9.
Cite as

Barbara M. Anthony, Sara Boyd, Ricky Birnbaum, Ananya Christman, Christine Chung, Patrick Davis, Jigar Dhimar, and David Yuen. Maximizing the Number of Rides Served for Dial-a-Ride. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{anthony_et_al:OASIcs.ATMOS.2019.11,
  author =	{Anthony, Barbara M. and Birnbaum, Ricky and Boyd, Sara and Christman, Ananya and Chung, Christine and Davis, Patrick and Dhimar, Jigar and Yuen, David},
  title =	{{Maximizing the Number of Rides Served for Dial-a-Ride}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{11:1--11:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.11},
  URN =		{urn:nbn:de:0030-drops-114237},
  doi =		{10.4230/OASIcs.ATMOS.2019.11},
  annote =	{Keywords: dial-a-ride, revenue maximization, approximation algorithm, vehicle routing}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.53
Extending the Centerpoint Theorem to Multiple Points

Authors: Alexander Pilz and Patrick Schnider

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
The centerpoint theorem is a well-known and widely used result in discrete geometry. It states that for any point set P of n points in R^d, there is a point c, not necessarily from P, such that each halfspace containing c contains at least n/(d+1) points of P. Such a point c is called a centerpoint, and it can be viewed as a generalization of a median to higher dimensions. In other words, a centerpoint can be interpreted as a good representative for the point set P. But what if we allow more than one representative? For example in one-dimensional data sets, often certain quantiles are chosen as representatives instead of the median. We present a possible extension of the concept of quantiles to higher dimensions. The idea is to find a set Q of (few) points such that every halfspace that contains one point of Q contains a large fraction of the points of P and every halfspace that contains more of Q contains an even larger fraction of P. This setting is comparable to the well-studied concepts of weak epsilon-nets and weak epsilon-approximations, where it is stronger than the former but weaker than the latter. We show that for any point set of size n in R^d and for any positive alpha_1,...,alpha_k where alpha_1 <= alpha_2 <= ... <= alpha_k and for every i,j with i+j <= k+1 we have that (d-1)alpha_k+alpha_i+alpha_j <= 1, we can find Q of size k such that each halfspace containing j points of Q contains least alpha_j n points of P. For two-dimensional point sets we further show that for every alpha and beta with alpha <= beta and alpha+beta <= 2/3 we can find Q with |Q|=3 such that each halfplane containing one point of Q contains at least alpha n of the points of P and each halfplane containing all of Q contains at least beta n points of P. All these results generalize to the setting where P is any mass distribution. For the case where P is a point set in R^2 and |Q|=2, we provide algorithms to find such points in time O(n log^3 n).
Cite as

Alexander Pilz and Patrick Schnider. Extending the Centerpoint Theorem to Multiple Points. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 53:1-53:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{pilz_et_al:LIPIcs.ISAAC.2018.53,
  author =	{Pilz, Alexander and Schnider, Patrick},
  title =	{{Extending the Centerpoint Theorem to Multiple Points}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{53:1--53:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.53},
  URN =		{urn:nbn:de:0030-drops-100019},
  doi =		{10.4230/LIPIcs.ISAAC.2018.53},
  annote =	{Keywords: centerpoint, point sets, Tukey depth}
}
Document
DOI: 10.4230/OASIcs.ICLP.2018.1
Epistemic Logic Programs with World View Constraints

Authors: Patrick Thor Kahl and Anthony P. Leclerc

Published in: OASIcs, Volume 64, Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018)

Abstract
An epistemic logic program is a set of rules written in the language of Epistemic Specifications, an extension of the language of answer set programming that provides for more powerful introspective reasoning through the use of modal operators K and M. We propose adding a new construct to Epistemic Specifications called a world view constraint that provides a universal device for expressing global constraints in the various versions of the language. We further propose the use of subjective literals (literals preceded by K or M) in rule heads as syntactic sugar for world view constraints. Additionally, we provide an algorithm for finding the world views of such programs.
Cite as

Patrick Thor Kahl and Anthony P. Leclerc. Epistemic Logic Programs with World View Constraints. In Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018). Open Access Series in Informatics (OASIcs), Volume 64, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kahl_et_al:OASIcs.ICLP.2018.1,
  author =	{Kahl, Patrick Thor and Leclerc, Anthony P.},
  title =	{{Epistemic Logic Programs with World View Constraints}},
  booktitle =	{Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018)},
  pages =	{1:1--1:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-090-3},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{64},
  editor =	{Dal Palu', Alessandro and Tarau, Paul and Saeedloei, Neda and Fodor, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ICLP.2018.1},
  URN =		{urn:nbn:de:0030-drops-98679},
  doi =		{10.4230/OASIcs.ICLP.2018.1},
  annote =	{Keywords: Epistemic Specifications, Epistemic Logic Programs, Constraints, World View Constraints, World View Rules, WV Facts, Answer Set Programming, Logic Programming}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2018.6
Universal Safety for Timed Petri Nets is PSPACE-complete

Authors: Parosh Aziz Abdulla, Mohamed Faouzi Atig, Radu Ciobanu, Richard Mayr, and Patrick Totzke

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract
A timed network consists of an arbitrary number of initially identical 1-clock timed automata, interacting via hand-shake communication. In this setting there is no unique central controller, since all automata are initially identical. We consider the universal safety problem for such controller-less timed networks, i.e., verifying that a bad event (enabling some given transition) is impossible regardless of the size of the network. This universal safety problem is dual to the existential coverability problem for timed-arc Petri nets, i.e., does there exist a number m of tokens, such that starting with m tokens in a given place, and none in the other places, some given transition is eventually enabled. We show that these problems are PSPACE-complete.
Cite as

Parosh Aziz Abdulla, Mohamed Faouzi Atig, Radu Ciobanu, Richard Mayr, and Patrick Totzke. Universal Safety for Timed Petri Nets is PSPACE-complete. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abdulla_et_al:LIPIcs.CONCUR.2018.6,
  author =	{Abdulla, Parosh Aziz and Atig, Mohamed Faouzi and Ciobanu, Radu and Mayr, Richard and Totzke, Patrick},
  title =	{{Universal Safety for Timed Petri Nets is PSPACE-complete}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.6},
  URN =		{urn:nbn:de:0030-drops-95447},
  doi =		{10.4230/LIPIcs.CONCUR.2018.6},
  annote =	{Keywords: timed networks, safety checking, Petri nets, coverability}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.GISCIENCE.2018.27
Deconstructed and Inverted Multi-Criteria Evaluation for On-The-Fly Scenario Development and Decision-Making (Short Paper)

Authors: Martin Geilhausen and Patrick Laube

Published in: LIPIcs, Volume 114, 10th International Conference on Geographic Information Science (GIScience 2018)

Abstract
We propose a variation of the conventional spatial multi-criteria evaluation workflow for suitability analysis that allows efficient on-the fly scenario development for decision-making. Our approach proposes to reconstruct the conventional MCE workflow in order to exclude computationally expensive geoprocessing from the iterative scenario development. We then introduce a procedure that replaces costly iterations of spatial operations with one off-line preprocessing step followed by iterations of much less computationally expensive database queries. We illustrate our approach for deconstructed and inverted multi-criteria analysis with a case study aiming at selecting suitable sites for wind turbines in the Swiss alps.
Cite as

Martin Geilhausen and Patrick Laube. Deconstructed and Inverted Multi-Criteria Evaluation for On-The-Fly Scenario Development and Decision-Making (Short Paper). In 10th International Conference on Geographic Information Science (GIScience 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 114, pp. 27:1-27:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{geilhausen_et_al:LIPIcs.GISCIENCE.2018.27,
  author =	{Geilhausen, Martin and Laube, Patrick},
  title =	{{Deconstructed and Inverted Multi-Criteria Evaluation for On-The-Fly Scenario Development and Decision-Making}},
  booktitle =	{10th International Conference on Geographic Information Science (GIScience 2018)},
  pages =	{27:1--27:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-083-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{114},
  editor =	{Winter, Stephan and Griffin, Amy and Sester, Monika},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GISCIENCE.2018.27},
  URN =		{urn:nbn:de:0030-drops-93558},
  doi =		{10.4230/LIPIcs.GISCIENCE.2018.27},
  annote =	{Keywords: Multi-criteria evaluation, efficiency, decision-making, data structures}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.8
Strict Ideal Completions of the Lambda Calculus

Authors: Patrick Bahr

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of strictness. To obtain infinitary normalisation and infinitary confluence properties for these calculi, Kennaway et al. extend beta-reduction with infinitely many `bot-rules', which contract meaningless terms directly to bot. Three of the resulting Böhm reduction calculi have unique infinitary normal forms corresponding to Böhm-like trees. In this paper we develop a corresponding theory of infinitary lambda calculi based on ideal completion instead of metric completion. We show that each of our calculi conservatively extends the corresponding metric-based calculus. Three of our calculi are infinitarily normalising and confluent; their unique infinitary normal forms are exactly the Böhm-like trees of the corresponding metric-based calculi. Our calculi dispense with the infinitely many bot-rules of the metric-based calculi. The fully non-strict calculus (called 111) consists of only beta-reduction, while the other two calculi (called 001 and 101) require two additional rules that precisely state their strictness properties: lambda x.bot -> bot (for 001) and bot M -> bot (for 001 and 101).
Cite as

Patrick Bahr. Strict Ideal Completions of the Lambda Calculus. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bahr:LIPIcs.FSCD.2018.8,
  author =	{Bahr, Patrick},
  title =	{{Strict Ideal Completions of the Lambda Calculus}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.8},
  URN =		{urn:nbn:de:0030-drops-91787},
  doi =		{10.4230/LIPIcs.FSCD.2018.8},
  annote =	{Keywords: lambda calculus, infinitary rewriting, B\"{o}hm trees, meaningless terms, confluence}
}
Document
DOI: 10.4230/LIPIcs.CPM.2016.20
Boxed Permutation Pattern Matching

Authors: Mika Amit, Philip Bille, Patrick Hagge Cording, Inge Li Gørtz, and Hjalte Wedel Vildhøj

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract
Given permutations T and P of length n and m, respectively, the Permutation Pattern Matching problem asks to find all m-length subsequences of T that are order-isomorphic to P. This problem has a wide range of applications but is known to be NP-hard. In this paper, we study the special case, where the goal is to only find the boxed subsequences of T that are order-isomorphic to P. This problem was introduced by Bruner and Lackner who showed that it can be solved in O(n^3) time. Cho et al. [CPM 2015] gave an O(n^2m) time algorithm and improved it to O(n^2 log m). In this paper we present a solution that uses only O(n^2) time. In general, there are instances where the output size is Omega(n^2) and hence our bound is optimal. To achieve our results, we introduce several new ideas including a novel reduction to 2D offline dominance counting. Our algorithm is surprisingly simple and straightforward to implement.
Cite as

Mika Amit, Philip Bille, Patrick Hagge Cording, Inge Li Gørtz, and Hjalte Wedel Vildhøj. Boxed Permutation Pattern Matching. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 20:1-20:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{amit_et_al:LIPIcs.CPM.2016.20,
  author =	{Amit, Mika and Bille, Philip and Hagge Cording, Patrick and Li G{\o}rtz, Inge and Wedel Vildh{\o}j, Hjalte},
  title =	{{Boxed Permutation Pattern Matching}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{20:1--20:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.20},
  URN =		{urn:nbn:de:0030-drops-60744},
  doi =		{10.4230/LIPIcs.CPM.2016.20},
  annote =	{Keywords: Permutation, Subsequence, Pattern Matching, Order Preserving, Boxed Mesh Pattern}
}
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