6 Search Results for "Berger, Peter"


Document
Many Visits TSP Revisited

Authors: Łukasz Kowalik, Shaohua Li, Wojciech Nadara, Marcin Smulewicz, and Magnus Wahlström

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


Abstract
We study the Many Visits TSP problem, where given a number k(v) for each of n cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits each city v exactly k(v) times. The currently fastest algorithm is due to Berger, Kozma, Mnich and Vincze [SODA 2019, TALG 2020] and runs in time and space O*(5ⁿ). They also show a polynomial space algorithm running in time O(16^{n+o(n)}). In this work, we show three main results: - A randomized polynomial space algorithm in time O*(2^n D), where D is the maximum distance between two cities. By using standard methods, this results in a (1+ε)-approximation in time O*(2ⁿε^{-1}). Improving the constant 2 in these results would be a major breakthrough, as it would result in improving the O*(2ⁿ)-time algorithm for Directed Hamiltonian Cycle, which is a 50 years old open problem. - A tight analysis of Berger et al.’s exponential space algorithm, resulting in an O*(4ⁿ) running time bound. - A new polynomial space algorithm, running in time O(7.88ⁿ).

Cite as

Łukasz Kowalik, Shaohua Li, Wojciech Nadara, Marcin Smulewicz, and Magnus Wahlström. Many Visits TSP Revisited. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{kowalik_et_al:LIPIcs.ESA.2020.66,
  author =	{Kowalik, {\L}ukasz and Li, Shaohua and Nadara, Wojciech and Smulewicz, Marcin and Wahlstr\"{o}m, Magnus},
  title =	{{Many Visits TSP Revisited}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{66:1--66:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.66},
  URN =		{urn:nbn:de:0030-drops-129329},
  doi =		{10.4230/LIPIcs.ESA.2020.66},
  annote =	{Keywords: many visits traveling salesman problem, exponential algorithm}
}
Document
Martin Hofmann’s Case for Non-Strictly Positive Data Types

Authors: Ulrich Berger, Ralph Matthes, and Anton Setzer

Published in: LIPIcs, Volume 130, 24th International Conference on Types for Proofs and Programs (TYPES 2018)


Abstract
We describe the breadth-first traversal algorithm by Martin Hofmann that uses a non-strictly positive data type and carry out a simple verification in an extensional setting. Termination is shown by implementing the algorithm in the strongly normalising extension of system F by Mendler-style recursion. We then analyze the same algorithm by alternative verifications first in an intensional setting using a non-strictly positive inductive definition (not just a non-strictly positive data type), and subsequently by two different algebraic reductions. The verification approaches are compared in terms of notions of simulation and should elucidate the somewhat mysterious algorithm and thus make a case for other uses of non-strictly positive data types. Except for the termination proof, which cannot be formalised in Coq, all proofs were formalised in Coq and some of the algorithms were implemented in Agda and Haskell.

Cite as

Ulrich Berger, Ralph Matthes, and Anton Setzer. Martin Hofmann’s Case for Non-Strictly Positive Data Types. In 24th International Conference on Types for Proofs and Programs (TYPES 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 130, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{berger_et_al:LIPIcs.TYPES.2018.1,
  author =	{Berger, Ulrich and Matthes, Ralph and Setzer, Anton},
  title =	{{Martin Hofmann’s Case for Non-Strictly Positive Data Types}},
  booktitle =	{24th International Conference on Types for Proofs and Programs (TYPES 2018)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-106-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{130},
  editor =	{Dybjer, Peter and Esp{\'\i}rito Santo, Jos\'{e} and Pinto, Lu{\'\i}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2018.1},
  URN =		{urn:nbn:de:0030-drops-114052},
  doi =		{10.4230/LIPIcs.TYPES.2018.1},
  annote =	{Keywords: non strictly-positive data types, breadth-first traversal, program verification, Mendler-style recursion, System F, theorem proving, Coq, Agda, Haskell}
}
Document
Modelling Homogeneous Generative Meta-Programming

Authors: Martin Berger, Laurence Tratt, and Christian Urban

Published in: LIPIcs, Volume 74, 31st European Conference on Object-Oriented Programming (ECOOP 2017)


Abstract
Homogeneous generative meta-programming (HGMP) enables the generation of program fragments at compile-time or run-time. We present a foundational calculus which can model both compile-time and run-time evaluated HGMP, allowing us to model, for the first time, languages such as Template Haskell. The calculus is designed such that it can be gradually enhanced with the features needed to model many of the advanced features of real languages. We demonstrate this by showing how a simple, staged type system as found in Template Haskell can be added to the calculus.

Cite as

Martin Berger, Laurence Tratt, and Christian Urban. Modelling Homogeneous Generative Meta-Programming. In 31st European Conference on Object-Oriented Programming (ECOOP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 74, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{berger_et_al:LIPIcs.ECOOP.2017.5,
  author =	{Berger, Martin and Tratt, Laurence and Urban, Christian},
  title =	{{Modelling Homogeneous Generative Meta-Programming}},
  booktitle =	{31st European Conference on Object-Oriented Programming (ECOOP 2017)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-035-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{74},
  editor =	{M\"{u}ller, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2017.5},
  URN =		{urn:nbn:de:0030-drops-72775},
  doi =		{10.4230/LIPIcs.ECOOP.2017.5},
  annote =	{Keywords: Formal Methods, Meta-Programming, Operational Semantics, Types, Quasi-Quotes, Abstract Syntax Trees}
}
Document
Realisability and Adequacy for (Co)induction

Authors: Ulrich Berger

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)


Abstract
We prove the correctness of a formalised realisability interpretation of extensions of first-order theories by inductive and coinductive definitions in an untyped $\lambda$-calculus with fixed-points. We illustrate the use of this interpretation for program extraction by some simple examples in the area of exact real number computation and hint at further non-trivial applications in computable analysis.

Cite as

Ulrich Berger. Realisability and Adequacy for (Co)induction. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 49-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{berger:OASIcs.CCA.2009.2258,
  author =	{Berger, Ulrich},
  title =	{{Realisability and Adequacy for (Co)induction}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{49--60},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2258},
  URN =		{urn:nbn:de:0030-drops-22581},
  doi =		{10.4230/OASIcs.CCA.2009.2258},
  annote =	{Keywords: Constructive Analysis, realisability, program extraction, semantics}
}
Document
A Constructive Study of Landau's Summability Theorem

Authors: Josef Berger and Douglas Bridges

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)


Abstract
A summability theorem of Landau, which classically is a simple consequence of the uniform boundedness theorem, is examined constructively.

Cite as

Josef Berger and Douglas Bridges. A Constructive Study of Landau's Summability Theorem. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 61-70, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{berger_et_al:OASIcs.CCA.2009.2259,
  author =	{Berger, Josef and Bridges, Douglas},
  title =	{{A Constructive Study of Landau's Summability Theorem}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{61--70},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2259},
  URN =		{urn:nbn:de:0030-drops-22595},
  doi =		{10.4230/OASIcs.CCA.2009.2259},
  annote =	{Keywords: Constructive analysis, Landau's theorem, uniform boundedness theorem Constructive analysis, Landau's theorem, uniform boundedness theorem}
}
Document
Glycosylation Patterns of Proteins Studied by Liquid Chromatography-Mass Spectrometry and Bioinformatic Tools

Authors: Hansjörg Toll, Peter Berger, Andreas Hofmann, Andreas Hildebrandt, Herbert Oberacher, Hans Peter Lenhof, and Christian G. Huber

Published in: Dagstuhl Seminar Proceedings, Volume 5471, Computational Proteomics (2006)


Abstract
Due to their extensive structural heterogeneity, the elucidation of glycosylation patterns in glycoproteins such as the subunits of chorionic gonadotropin (CG), CG-alpha and CG-beta remains one of the most challenging problems in the proteomic analysis of posttranslational modifications. In consequence, glycosylation is usually studied after decomposition of the intact proteins to the proteolytic peptide level. However, by this approach all information about the combination of the different glycopeptides in the intact protein is lost. In this study we have, therefore, attempted to combine the results of glycan identification after tryptic digestion with molecular mass measurements on the intact glycoproteins. Despite the extremely high number of possible combinations of the glycans identified in the tryptic peptides by high-performance liquid chromatography-mass spectrometry (> 1000 for CG-alpha and > 10.000 for CG-beta), the mass spectra of intact CG-alpha and CG-beta revealed only a limited number of glycoforms present in CG preparations from pools of pregnancy urines. Peak annotations for CG-alpha were performed with the help of an algorithm that generates a database containing all possible modifications of the proteins (inclusive possible artificial modifications such as oxidation or truncation) and subsequent searches for combinations fitting the mass difference between the polypeptide backbone and the measured molecular masses. Fourteen different glycoforms of CG-alpha, including methionine-oxidized and N-terminally truncated forms, were readily identified. For CG-beta, however, the relatively high mass accuracy of ± 2 Da was still insufficient to unambiguously assign the possible combinations of posttranslational modifications. Finally, the mass spectrometric fingerprints of the intact molecules were shown to be very useful for the characterization of glycosylation patterns in different CG preparations.

Cite as

Hansjörg Toll, Peter Berger, Andreas Hofmann, Andreas Hildebrandt, Herbert Oberacher, Hans Peter Lenhof, and Christian G. Huber. Glycosylation Patterns of Proteins Studied by Liquid Chromatography-Mass Spectrometry and Bioinformatic Tools. In Computational Proteomics. Dagstuhl Seminar Proceedings, Volume 5471, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@InProceedings{toll_et_al:DagSemProc.05471.8,
  author =	{Toll, Hansj\"{o}rg and Berger, Peter and Hofmann, Andreas and Hildebrandt, Andreas and Oberacher, Herbert and Lenhof, Hans Peter and Huber, Christian G.},
  title =	{{Glycosylation Patterns of Proteins Studied by Liquid Chromatography-Mass Spectrometry and Bioinformatic Tools}},
  booktitle =	{Computational Proteomics},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5471},
  editor =	{Christian G. Huber and Oliver Kohlbacher and Knut Reinert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05471.8},
  URN =		{urn:nbn:de:0030-drops-5431},
  doi =		{10.4230/DagSemProc.05471.8},
  annote =	{Keywords: Liquid chromatography, mass spectrometry, glycoproteins, glycosylation, peak annotation}
}
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