141 Search Results for "J�nger, Michael"

Document
DOI: 10.4230/LIPIcs.ICDT.2024.13
Direct Access for Conjunctive Queries with Negations

Authors: Florent Capelli and Oliver Irwin

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

Abstract
Given a conjunctive query Q and a database 𝐃, a direct access to the answers of Q over 𝐃 is the operation of returning, given an index j, the j-th answer for some order on its answers. While this problem is #P-hard in general with respect to combined complexity, many conjunctive queries have an underlying structure that allows for a direct access to their answers for some lexicographical ordering that takes polylogarithmic time in the size of the database after a polynomial time precomputation. Previous work has precisely characterised the tractable classes and given fine-grained lower bounds on the precomputation time needed depending on the structure of the query. In this paper, we generalise these tractability results to the case of signed conjunctive queries, that is, conjunctive queries that may contain negative atoms. Our technique is based on a class of circuits that can represent relational data. We first show that this class supports tractable direct access after a polynomial time preprocessing. We then give bounds on the size of the circuit needed to represent the answer set of signed conjunctive queries depending on their structure. Both results combined together allow us to prove the tractability of direct access for a large class of conjunctive queries. On the one hand, we recover the known tractable classes from the literature in the case of positive conjunctive queries. On the other hand, we generalise and unify known tractability results about negative conjunctive queries - that is, queries having only negated atoms. In particular, we show that the class of β-acyclic negative conjunctive queries and the class of bounded nest set width negative conjunctive queries admit tractable direct access.
Cite as

Florent Capelli and Oliver Irwin. Direct Access for Conjunctive Queries with Negations. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{capelli_et_al:LIPIcs.ICDT.2024.13,
  author =	{Capelli, Florent and Irwin, Oliver},
  title =	{{Direct Access for Conjunctive Queries with Negations}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.13},
  URN =		{urn:nbn:de:0030-drops-197958},
  doi =		{10.4230/LIPIcs.ICDT.2024.13},
  annote =	{Keywords: Conjunctive queries, factorized databases, direct access, hypertree decomposition}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2024.18
Computing Data Distribution from Query Selectivities

Authors: Pankaj K. Agarwal, Rahul Raychaudhury, Stavros Sintos, and Jun Yang

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

Abstract
We are given a set 𝒵 = {(R_1,s_1), …, (R_n,s_n)}, where each R_i is a range in ℝ^d, such as rectangle or ball, and s_i ∈ [0,1] denotes its selectivity. The goal is to compute a small-size discrete data distribution 𝒟 = {(q₁,w₁),…, (q_m,w_m)}, where q_j ∈ ℝ^d and w_j ∈ [0,1] for each 1 ≤ j ≤ m, and ∑_{1≤j≤m} w_j = 1, such that 𝒟 is the most consistent with 𝒵, i.e., err_p(𝒟,𝒵) = 1/n ∑_{i = 1}ⁿ |s_i - ∑_{j=1}^m w_j⋅1(q_j ∈ R_i)|^p is minimized. In a database setting, 𝒵 corresponds to a workload of range queries over some table, together with their observed selectivities (i.e., fraction of tuples returned), and 𝒟 can be used as compact model for approximating the data distribution within the table without accessing the underlying contents. In this paper, we obtain both upper and lower bounds for this problem. In particular, we show that the problem of finding the best data distribution from selectivity queries is NP-complete. On the positive side, we describe a Monte Carlo algorithm that constructs, in time O((n+δ^{-d}) δ^{-2} polylog n), a discrete distribution 𝒟̃ of size O(δ^{-2}), such that err_p(𝒟̃,𝒵) ≤ min_𝒟 err_p(𝒟,𝒵)+δ (for p = 1,2,∞) where the minimum is taken over all discrete distributions. We also establish conditional lower bounds, which strongly indicate the infeasibility of relative approximations as well as removal of the exponential dependency on the dimension for additive approximations. This suggests that significant improvements to our algorithm are unlikely.
Cite as

Pankaj K. Agarwal, Rahul Raychaudhury, Stavros Sintos, and Jun Yang. Computing Data Distribution from Query Selectivities. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{agarwal_et_al:LIPIcs.ICDT.2024.18,
  author =	{Agarwal, Pankaj K. and Raychaudhury, Rahul and Sintos, Stavros and Yang, Jun},
  title =	{{Computing Data Distribution from Query Selectivities}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.18},
  URN =		{urn:nbn:de:0030-drops-198007},
  doi =		{10.4230/LIPIcs.ICDT.2024.18},
  annote =	{Keywords: selectivity queries, discrete distributions, Multiplicative Weights Update, eps-approximation, learnable functions, depth problem, arrangement}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.6
Facility Location in the Sublinear Geometric Model

Authors: Morteza Monemizadeh

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
In the sublinear geometric model, we are provided with an oracle access to a point set P of n points in a bounded discrete space [Δ]², where Δ = n^O(1) is a polynomially bounded number in n. That is, we do not have direct access to the points, but we can make certain types of queries and there is an oracle that responds to our queries. The type of queries that we assume we can make in this paper, are range counting queries where ranges are axis-aligned rectangles (that are basic primitives in database [Srikanta Tirthapura and David P. Woodruff, 2012; Bentley, 1975; Mark de Berg et al., 2008], computational geometry [Pankaj K. Agarwal, 2004; Pankaj K. Agarwal et al., 1996; Boris Aronov et al., 2010; Boris Aronov et al., 2009], and machine learning [Menachem Sadigurschi and Uri Stemmer, 2021; Long and Tan, 1998; Michael J. Kearns and Umesh V. Vazirani, 1995; Michael J. Kearns and Umesh V. Vazirani, 1994]). The oracle then answers these queries by returning the number of points that are in queried ranges. Let {Alg} be an algorithm that (exactly or approximately) solves a problem 𝒫 in the sublinear geometric model. The query complexity of Alg is measured in terms of the number of queries that Alg makes to solve 𝒫. In this paper, we study the complexity of the (uniform) Euclidean facility location problem in the sublinear geometric model. We develop a randomized sublinear algorithm that with high probability, (1+ε)-approximates the cost of the Euclidean facility location problem of the point set P in the sublinear geometric model using Õ(√n) range counting queries. We complement this result by showing that approximating the cost of the Euclidean facility location problem within o(log(n))-factor in the sublinear geometric model using the sampling strategy that we propose for our sublinear algorithm needs Ω̃(n^{1/4}) RangeCount queries. We leave it as an open problem whether such a polynomial lower bound on the number of RangeCount queries exists for any randomized sublinear algorithm that approximates the cost of the facility location problem within a constant factor.
Cite as

Morteza Monemizadeh. Facility Location in the Sublinear Geometric Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 6:1-6:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{monemizadeh:LIPIcs.APPROX/RANDOM.2023.6,
  author =	{Monemizadeh, Morteza},
  title =	{{Facility Location in the Sublinear Geometric Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{6:1--6:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  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.2023.6},
  URN =		{urn:nbn:de:0030-drops-188315},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.6},
  annote =	{Keywords: Facility Location, Sublinear Geometric Model, Range Counting Queries}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.9
Axis-Parallel Right Angle Crossing Graphs

Authors: Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.
Cite as

Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt. Axis-Parallel Right Angle Crossing Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{angelini_et_al:LIPIcs.ESA.2023.9,
  author =	{Angelini, Patrizio and Bekos, Michael A. and Katheder, Julia and Kaufmann, Michael and Pfister, Maximilian and Ueckerdt, Torsten},
  title =	{{Axis-Parallel Right Angle Crossing Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.9},
  URN =		{urn:nbn:de:0030-drops-186623},
  doi =		{10.4230/LIPIcs.ESA.2023.9},
  annote =	{Keywords: Graph drawing, RAC graphs, Graph drawing algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.10
(No) Quantum Space-Time Tradeoff for USTCON

Authors: Simon Apers, Stacey Jeffery, Galina Pass, and Michael Walter

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Undirected st-connectivity is important both for its applications in network problems, and for its theoretical connections with logspace complexity. Classically, a long line of work led to a time-space tradeoff of T = Õ(n²/S) for any S such that S = Ω(log(n)) and S = O(n²/m). Surprisingly, we show that quantumly there is no nontrivial time-space tradeoff: there is a quantum algorithm that achieves both optimal time Õ(n) and space O(log(n)) simultaneously. This improves on previous results, which required either O(log(n)) space and Õ(n^{1.5}) time, or Õ(n) space and time. To complement this, we show that there is a nontrivial time-space tradeoff when given a lower bound on the spectral gap of a corresponding random walk.
Cite as

Simon Apers, Stacey Jeffery, Galina Pass, and Michael Walter. (No) Quantum Space-Time Tradeoff for USTCON. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{apers_et_al:LIPIcs.ESA.2023.10,
  author =	{Apers, Simon and Jeffery, Stacey and Pass, Galina and Walter, Michael},
  title =	{{(No) Quantum Space-Time Tradeoff for USTCON}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.10},
  URN =		{urn:nbn:de:0030-drops-186636},
  doi =		{10.4230/LIPIcs.ESA.2023.10},
  annote =	{Keywords: Undirected st-connectivity, quantum walks, time-space tradeoff}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.28
On k-Means for Segments and Polylines

Authors: Sergio Cabello and Panos Giannopoulos

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We study the problem of k-means clustering in the space of straight-line segments in ℝ² under the Hausdorff distance. For this problem, we give a (1+ε)-approximation algorithm that, for an input of n segments, for any fixed k, and with constant success probability, runs in time O(n + ε^{-O(k)} + ε^{-O(k)} ⋅ log^O(k) (ε^{-1})). The algorithm has two main ingredients. Firstly, we express the k-means objective in our metric space as a sum of algebraic functions and use the optimization technique of Vigneron [Antoine Vigneron, 2014] to approximate its minimum. Secondly, we reduce the input size by computing a small size coreset using the sensitivity-based sampling framework by Feldman and Langberg [Dan Feldman and Michael Langberg, 2011; Feldman et al., 2020]. Our results can be extended to polylines of constant complexity with a running time of O(n + ε^{-O(k)}).
Cite as

Sergio Cabello and Panos Giannopoulos. On k-Means for Segments and Polylines. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{cabello_et_al:LIPIcs.ESA.2023.28,
  author =	{Cabello, Sergio and Giannopoulos, Panos},
  title =	{{On k-Means for Segments and Polylines}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{28:1--28:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.28},
  URN =		{urn:nbn:de:0030-drops-186812},
  doi =		{10.4230/LIPIcs.ESA.2023.28},
  annote =	{Keywords: k-means clustering, segments, polylines, Hausdorff distance, Fr\'{e}chet mean}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.36
Robust and Space-Efficient Dual Adversary Quantum Query Algorithms

Authors: Michael Czekanski, Shelby Kimmel, and R. Teal Witter

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
The general adversary dual is a powerful tool in quantum computing because it gives a query-optimal bounded-error quantum algorithm for deciding any Boolean function. Unfortunately, the algorithm uses linear qubits in the worst case, and only works if the constraints of the general adversary dual are exactly satisfied. The challenge of improving the algorithm is that it is brittle to arbitrarily small errors since it relies on a reflection over a span of vectors. We overcome this challenge and build a robust dual adversary algorithm that can handle approximately satisfied constraints. As one application of our robust algorithm, we prove that for any Boolean function with polynomially many 1-valued inputs (or in fact a slightly weaker condition) there is a query-optimal algorithm that uses logarithmic qubits. As another application, we prove that numerically derived, approximate solutions to the general adversary dual give a bounded-error quantum algorithm under certain conditions. Further, we show that these conditions empirically hold with reasonable iterations for Boolean functions with small domains. We also develop several tools that may be of independent interest, including a robust approximate spectral gap lemma, a method to compress a general adversary dual solution using the Johnson-Lindenstrauss lemma, and open-source code to find solutions to the general adversary dual.
Cite as

Michael Czekanski, Shelby Kimmel, and R. Teal Witter. Robust and Space-Efficient Dual Adversary Quantum Query Algorithms. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{czekanski_et_al:LIPIcs.ESA.2023.36,
  author =	{Czekanski, Michael and Kimmel, Shelby and Witter, R. Teal},
  title =	{{Robust and Space-Efficient Dual Adversary Quantum Query Algorithms}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{36:1--36:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.36},
  URN =		{urn:nbn:de:0030-drops-186890},
  doi =		{10.4230/LIPIcs.ESA.2023.36},
  annote =	{Keywords: Quantum Computing, Robust Quantum Algorithms, Johnson-Lindenstrauss Lemma, Span Programs, Query Complexity, Space Complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.45
The Lawn Mowing Problem: From Algebra to Algorithms

Authors: Sándor P. Fekete, Dominik Krupke, Michael Perk, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
For a given polygonal region P, the Lawn Mowing Problem (LMP) asks for a shortest tour T that gets within Euclidean distance 1/2 of every point in P; this is equivalent to computing a shortest tour for a unit-diameter cutter C that covers all of P. As a generalization of the Traveling Salesman Problem, the LMP is NP-hard; unlike the discrete TSP, however, the LMP has defied efforts to achieve exact solutions, due to its combination of combinatorial complexity with continuous geometry. We provide a number of new contributions that provide insights into the involved difficulties, as well as positive results that enable both theoretical and practical progress. (1) We show that the LMP is algebraically hard: it is not solvable by radicals over the field of rationals, even for the simple case in which P is a 2×2 square. This implies that it is impossible to compute exact optimal solutions under models of computation that rely on elementary arithmetic operations and the extraction of kth roots, and explains the perceived practical difficulty. (2) We exploit this algebraic analysis for the natural class of polygons with axis-parallel edges and integer vertices (i.e., polyominoes), highlighting the relevance of turn-cost minimization for Lawn Mowing tours, and leading to a general construction method for feasible tours. (3) We show that this construction method achieves theoretical worst-case guarantees that improve previous approximation factors for polyominoes. (4) We demonstrate the practical usefulness beyond polyominoes by performing an extensive practical study on a spectrum of more general benchmark polygons: We obtain solutions that are better than the previous best values by Fekete et al., for instance sizes up to 20 times larger.
Cite as

Sándor P. Fekete, Dominik Krupke, Michael Perk, Christian Rieck, and Christian Scheffer. The Lawn Mowing Problem: From Algebra to Algorithms. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{fekete_et_al:LIPIcs.ESA.2023.45,
  author =	{Fekete, S\'{a}ndor P. and Krupke, Dominik and Perk, Michael and Rieck, Christian and Scheffer, Christian},
  title =	{{The Lawn Mowing Problem: From Algebra to Algorithms}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{45:1--45:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.45},
  URN =		{urn:nbn:de:0030-drops-186985},
  doi =		{10.4230/LIPIcs.ESA.2023.45},
  annote =	{Keywords: Geometric optimization, covering problems, tour problems, lawn mowing, algebraic hardness, approximation algorithms, algorithm engineering}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.77
Structural Parameterizations for Two Bounded Degree Problems Revisited

Authors: Michael Lampis and Manolis Vasilakis

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We revisit two well-studied problems, Bounded Degree Vertex Deletion and Defective Coloring, where the input is a graph G and a target degree Δ and we are asked either to edit or partition the graph so that the maximum degree becomes bounded by Δ. Both problems are known to be parameterized intractable for the most well-known structural parameters, such as treewidth. We revisit the parameterization by treewidth, as well as several related parameters and present a more fine-grained picture of the complexity of both problems. In particular: - Both problems admit straightforward DP algorithms with table sizes (Δ+2)^tw and (χ_d(Δ+1))^{tw} respectively, where tw is the input graph’s treewidth and χ_d the number of available colors. We show that, under the SETH, both algorithms are essentially optimal, for any non-trivial fixed values of Δ, χ_d, even if we replace treewidth by pathwidth. Along the way, we obtain an algorithm for Defective Coloring with complexity quasi-linear in the table size, thus settling the complexity of both problems for treewidth and pathwidth. - Given that the standard DP algorithm is optimal for treewidth and pathwidth, we then go on to consider the more restricted parameter tree-depth. Here, previously known lower bounds imply that, under the ETH, Bounded Vertex Degree Deletion and Defective Coloring cannot be solved in time n^o(∜{td}) and n^o(√{td}) respectively, leaving some hope that a qualitatively faster algorithm than the one for treewidth may be possible. We close this gap by showing that neither problem can be solved in time n^o(td), under the ETH, by employing a recursive low tree-depth construction that may be of independent interest. - Finally, we consider a structural parameter that is known to be restrictive enough to render both problems FPT: vertex cover. For both problems the best known algorithm in this setting has a super-exponential dependence of the form vc^𝒪(vc). We show that this is optimal, as an algorithm with dependence of the form vc^o(vc) would violate the ETH. Our proof relies on a new application of the technique of d-detecting families introduced by Bonamy et al. [ToCT 2019]. Our results, although mostly negative in nature, paint a clear picture regarding the complexity of both problems in the landscape of parameterized complexity, since in all cases we provide essentially matching upper and lower bounds.
Cite as

Michael Lampis and Manolis Vasilakis. Structural Parameterizations for Two Bounded Degree Problems Revisited. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 77:1-77:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{lampis_et_al:LIPIcs.ESA.2023.77,
  author =	{Lampis, Michael and Vasilakis, Manolis},
  title =	{{Structural Parameterizations for Two Bounded Degree Problems Revisited}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{77:1--77:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.77},
  URN =		{urn:nbn:de:0030-drops-187302},
  doi =		{10.4230/LIPIcs.ESA.2023.77},
  annote =	{Keywords: ETH, Parameterized Complexity, SETH}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2023.4
Algebraic Reasoning for (Un)Solvable Loops (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Loop invariants describe valid program properties that hold before and after every loop iteration. As such, loop invariants are the workhorses in formalizing loop semantics and automating the formal analysis and verification of programs with loops. While automatically synthesizing loop invariants is, in general, an uncomputable problem, when considering only single-path loops with linear updates (linear loops), the strongest polynomial invariant is in fact computable [Michael Karr, 1976; Markus Müller-Olm and Helmut Seidl, 2004; Laura Kovács, 2008; Ehud Hrushovski et al., 2018]. Yet, already for loops with "only" polynomial updates, computing the strongest invariant has been an open challenge since 2004 [Markus Müller-Olm and Helmut Seidl, 2004]. In this invited talk, we first present computability results on polynomial invariant synthesis for restricted polynomial loops, called solvable loops [Rodríguez-Carbonell and Kapur, 2004]. Key to solvable loops is that one can automatically compute invariants from closed-form solutions of algebraic recurrence equations that model the loop behaviour [Laura Kovács, 2008; Andreas Humenberger et al., 2017]. We also establish a technique for invariant synthesis for classes of loops that are not solvable, termed unsolvable loops [Daneshvar Amrollahi et al., 2022]. We next study the limits of computability in deriving the (strongest) polynomial invariants for arbitrary polynomial loops. We prove that computing the strongest polynomial invariant of arbitrary, single-path polynomial loops is very hard [Julian Müllner, 2023] - namely, it is at least as hard as the Skolem problem [Graham Everest et al., 2003; Terrence Tao, 2008], a prominent algebraic problem in the theory of linear recurrences. Going beyond single-path loops, we show that the strongest polynomial invariant is uncomputable already for multi-path polynomial loops with arbitrary quadratic polynomial updates [Laura Kovács and Anton Varonka, 2023].
Cite as

Laura Kovács. Algebraic Reasoning for (Un)Solvable Loops (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 4:1-4:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.MFCS.2023.4,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Algebraic Reasoning for (Un)Solvable Loops}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{4:1--4:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.4},
  URN =		{urn:nbn:de:0030-drops-185385},
  doi =		{10.4230/LIPIcs.MFCS.2023.4},
  annote =	{Keywords: Symbolic Computation, Formal Methods, Loop Analysis, Polynomial Invariants}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.25
Deterministic Constrained Multilinear Detection

Authors: Cornelius Brand, Viktoriia Korchemna, and Michael Skotnica

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
We extend the algebraic techniques of Brand and Pratt (ICALP'21) for deterministic detection of k-multilinear monomials in a given polynomial with non-negative coefficients to the more general situation of detecting colored k-multilinear monomials that satisfy additional constraints on the multiplicities of the colors appearing in them. Our techniques can be viewed as a characteristic-zero generalization of the algebraic tools developed by Guillemot and Sikora (MFCS'10) and Björklund, Kaski and Kowalik (STACS'13) As applications, we recover the state-of-the-art deterministic algorithms for the Graph Motif problem due to Pinter, Schachnai and Zehavi (MFCS'14), and give new deterministic algorithms for generalizations of certain questions on colored directed spanning trees or bipartite planar matchings running in deterministic time O^∗(4^k), studied originally by Gutin, Reidl, Wahlström and Zehavi (J. Comp. Sys. Sci. 95, '18). Finally, we give improved randomized algorithms for intersecting three and four matroids of rank k in characteristic zero, improving the record bounds of Brand and Pratt (ICALP'21) from O^∗(64^k) and O^∗(256^k), respectively, to O^∗(4^k).
Cite as

Cornelius Brand, Viktoriia Korchemna, and Michael Skotnica. Deterministic Constrained Multilinear Detection. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{brand_et_al:LIPIcs.MFCS.2023.25,
  author =	{Brand, Cornelius and Korchemna, Viktoriia and Skotnica, Michael},
  title =	{{Deterministic Constrained Multilinear Detection}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.25},
  URN =		{urn:nbn:de:0030-drops-185595},
  doi =		{10.4230/LIPIcs.MFCS.2023.25},
  annote =	{Keywords: Fixed-parameter algorithms, Algebraic algorithms, Motif discovery, Matroid intersection}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.28
Short Definitions in Constraint Languages

Authors: Jakub Bulín and Michael Kompatscher

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
A first-order formula is called primitive positive (pp) if it only admits the use of existential quantifiers and conjunction. Pp-formulas are a central concept in (fixed-template) constraint satisfaction since CSP(Γ) can be viewed as the problem of deciding the primitive positive theory of Γ, and pp-definability captures gadget reductions between CSPs. An important class of tractable constraint languages Γ is characterized by having few subpowers, that is, the number of n-ary relations pp-definable from Γ is bounded by 2^p(n) for some polynomial p(n). In this paper we study a restriction of this property, stating that every pp-definable relation is definable by a pp-formula of polynomial length. We conjecture that the existence of such short definitions is actually equivalent to Γ having few subpowers, and verify this conjecture for a large subclass that, in particular, includes all constraint languages on three-element domains. We furthermore discuss how our conjecture imposes an upper complexity bound of co-NP on the subpower membership problem of algebras with few subpowers.
Cite as

Jakub Bulín and Michael Kompatscher. Short Definitions in Constraint Languages. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bulin_et_al:LIPIcs.MFCS.2023.28,
  author =	{Bul{\'\i}n, Jakub and Kompatscher, Michael},
  title =	{{Short Definitions in Constraint Languages}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.28},
  URN =		{urn:nbn:de:0030-drops-185629},
  doi =		{10.4230/LIPIcs.MFCS.2023.28},
  annote =	{Keywords: constraint satisfaction, primitive positive definability, few subpowers, polynomially expressive, relational clone, subpower membership}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.30
Parikh One-Counter Automata

Authors: Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Counting abilities in finite automata are traditionally provided by two orthogonal extensions: adding a single counter that can be tested for zeroness at any point, or adding ℤ-valued counters that are tested for equality only at the end of runs. In this paper, finite automata extended with both types of counters are introduced. They are called Parikh One-Counter Automata (POCA): the "Parikh" part referring to the evaluation of counters at the end of runs, and the "One-Counter" part to the single counter that can be tested during runs. Their expressiveness, in the deterministic and nondeterministic variants, is investigated; it is shown in particular that there are deterministic POCA languages that cannot be expressed without nondeterminism in the original models. The natural decision problems are also studied; strikingly, most of them are no harder than in the original models. A parametric version of nonemptiness is also considered.
Cite as

Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha. Parikh One-Counter Automata. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{cadilhac_et_al:LIPIcs.MFCS.2023.30,
  author =	{Cadilhac, Micha\"{e}l and Ghosh, Arka and P\'{e}rez, Guillermo A. and Raha, Ritam},
  title =	{{Parikh One-Counter Automata}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.30},
  URN =		{urn:nbn:de:0030-drops-185645},
  doi =		{10.4230/LIPIcs.MFCS.2023.30},
  annote =	{Keywords: Parikh automata, Context-free languages, One-counter automata}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.62
Parameterized Max Min Feedback Vertex Set

Authors: Michael Lampis, Nikolaos Melissinos, and Manolis Vasilakis

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters. Using standard DP techniques, we first present an algorithm of time tw^O(tw) n^O(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vc^O(vc) n^O(1), where tw, vc denote the input graph’s treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc^o(vc) n^O(1) algorithm would refute the ETH. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10^k n^O(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34^k n^O(1).
Cite as

Michael Lampis, Nikolaos Melissinos, and Manolis Vasilakis. Parameterized Max Min Feedback Vertex Set. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 62:1-62:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{lampis_et_al:LIPIcs.MFCS.2023.62,
  author =	{Lampis, Michael and Melissinos, Nikolaos and Vasilakis, Manolis},
  title =	{{Parameterized Max Min Feedback Vertex Set}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{62:1--62:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.62},
  URN =		{urn:nbn:de:0030-drops-185965},
  doi =		{10.4230/LIPIcs.MFCS.2023.62},
  annote =	{Keywords: ETH, Feedback vertex set, Parameterized algorithms, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.65
A Weyl Criterion for Finite-State Dimension and Applications

Authors: Jack H. Lutz, Satyadev Nandakumar, and Subin Pulari

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Finite-state dimension, introduced early in this century as a finite-state version of classical Hausdorff dimension, is a quantitative measure of the lower asymptotic density of information in an infinite sequence over a finite alphabet, as perceived by finite automata. Finite-state dimension is a robust concept that now has equivalent formulations in terms of finite-state gambling, lossless finite-state data compression, finite-state prediction, entropy rates, and automatic Kolmogorov complexity. The 1972 Schnorr-Stimm dichotomy theorem gave the first automata-theoretic characterization of normal sequences, which had been studied in analytic number theory since Borel defined them in 1909. This theorem implies, in present-day terminology, that a sequence (or a real number having this sequence as its base-b expansion) is normal if and only if it has finite-state dimension 1. One of the most powerful classical tools for investigating normal numbers is the 1916 Weyl’s criterion, which characterizes normality in terms of exponential sums. Such sums are well studied objects with many connections to other aspects of analytic number theory, and this has made use of Weyl’s criterion especially fruitful. This raises the question whether Weyl’s criterion can be generalized from finite-state dimension 1 to arbitrary finite-state dimensions, thereby making it a quantitative tool for studying data compression, prediction, etc. i.e., Can we characterize all compression ratios using exponential sums?. This paper does exactly this. We extend Weyl’s criterion from a characterization of sequences with finite-state dimension 1 to a criterion that characterizes every finite-state dimension. This turns out not to be a routine generalization of the original Weyl criterion. Even though exponential sums may diverge for non-normal numbers, finite-state dimension can be characterized in terms of the dimensions of the subsequence limits of the exponential sums. In case the exponential sums are convergent, they converge to the Fourier coefficients of a probability measure whose dimension is precisely the finite-state dimension of the sequence. This new and surprising connection helps us bring Fourier analytic techniques to bear in proofs in finite-state dimension, yielding a new perspective. We demonstrate the utility of our criterion by substantially improving known results about preservation of finite-state dimension under arithmetic. We strictly generalize the results by Aistleitner and Doty, Lutz and Nandakumar for finite-state dimensions under arithmetic operations. We use the method of exponential sums and our Weyl criterion to obtain the following new result: If y is a number having finite-state strong dimension 0, then dim_FS(x+qy) = dim_FS(x) and Dim_FS(x+qy) = Dim_FS(x) for any x ∈ ℝ and q ∈ ℚ. This generalization uses recent estimates obtained in the work of Hochman [Hochman, 2014] regarding the entropy of convolutions of probability measures.
Cite as

Jack H. Lutz, Satyadev Nandakumar, and Subin Pulari. A Weyl Criterion for Finite-State Dimension and Applications. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 65:1-65:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{lutz_et_al:LIPIcs.MFCS.2023.65,
  author =	{Lutz, Jack H. and Nandakumar, Satyadev and Pulari, Subin},
  title =	{{A Weyl Criterion for Finite-State Dimension and Applications}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{65:1--65:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.65},
  URN =		{urn:nbn:de:0030-drops-185997},
  doi =		{10.4230/LIPIcs.MFCS.2023.65},
  annote =	{Keywords: Finite-state dimension, Finite-state compression, Weyl’s criterion, Exponential sums, Normal numbers}
}
  • Refine by Author
  • 6 Jünger, Michael
  • 5 Kaufmann, Michael
  • 4 Bekos, Michael A.
  • 4 Wallner, Michael
  • 3 Krämer, Bernd J.
  • Show More...

  • Refine by Classification
  • 8 Theory of computation → Computational geometry
  • 5 Theory of computation → Design and analysis of algorithms
  • 4 Mathematics of computing → Generating functions
  • 3 Mathematics of computing → Enumeration
  • 3 Mathematics of computing → Graphs and surfaces
  • Show More...

  • Refine by Keyword
  • 3 ETH
  • 3 graph algorithms
  • 3 graph drawing
  • 2 Approximation Algorithms
  • 2 Data mining
  • Show More...

  • Refine by Type
  • 141 document

  • Refine by Publication Year
  • 24 2006
  • 19 2023
  • 11 2016
  • 9 2008
  • 9 2017
  • Show More...

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact