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Project: Asymptotic Analysis of Extremal Discret...

Master data

German

Title:	Asymptotic Analysis of Extremal Discrete Structures
Description:	Strukturen oder Algorithmen zu optimieren, ist in verschiedenen Bereichen der Mathematik und ihrer Anwendungen von Bedeutung. Dabei sind nicht nur die Lösungen selbst von Interesse, sondern auch ihr qualitatives und quantitatives Verhalten für große Parameterwerte, wodurch ein besseres Verständnis ihrer Eigenschaften sowie ein Vergleich mit anderen Ansätzen und Strategien ermöglicht wird. Dies erfordert jedoch eine genaue asymptotische und probabilistische Analyse diskreter Strukturen und Algorithmen. In diesem Kontext interessieren wir uns besonders für mathematische Probleme aus der Graphentheorie und aus Anwendungen in der Kryptographie.
Keywords:	Digital expansions, Elliptic and hyperelliptic curve cryptography, Extremal discrete structures, Analysis of algorithms, Graph theoretic indices

Short title:	n.a.
Period:	15.01.2013 - 14.01.2018
Contact e-mail:	-
Homepage:	https://www.math.aau.at/P24644-N26/

Employees

Role

Time period

(internal)

Project leader

15.01.2013 - 14.01.2018

(internal)

PhD student

03.06.2013 - 30.06.2016

(internal)

PhD student

15.01.2013 - 28.02.2015

(internal)

PhD student
Research staff

15.01.2013 - 07.10.2015
08.10.2015 - 14.01.2016

(external)

Cooperation partner

15.01.2013 - 14.01.2018

(internal)

Student staff
PhD student

01.02.2015 - 31.08.2015
01.09.2015 - 14.01.2018

(internal)

Student staff

18.10.2017 - 14.01.2018

(internal)

Student staff

01.10.2017 - 14.01.2018

(internal)

Student staff

01.03.2017 - 31.08.2017

(internal)

Student staff

01.03.2017 - 31.08.2017

Assignment

Organisational unit

Fakultät für Technische Wissenschaften

Categorisation

Project type	Research funding (on request / by call for proposals)
Funding type	§26
Research type	Fundamental research
Subject areas	101024 - Probability theory 101025 - Number theory 101012 - Combinatorics 102016 - IT security
Research Cluster	No research Research Cluster selected
Gender aspects	0%
Project focus	Science to Science (Quality indicator: I) Classification raster of the assigned organisational units: Institut für Mathematik
working groups	No working group selected

Funding

Funding program

Cooperations

Organisation

Address

Rechbauerstraße 12
AT - 8010 Graz

S:t Olofsgatan 10B
SE - 75105 Uppsala

TW 115 Taipei

Ehrenbergstraße 29
DE - 98693 Ilmenau

Keplerstraße 7
DE - 70565 Stuttgart

420 University Blvd.
GB

ZA 7602 Stellenbosch

Research activities

All related research activities to this project are shown here. With the link below, you can view them in the search view where you are also able to export them.

Projects	No related projects
Publications	Symmetric digit sets for elliptic curve scalar multiplication without precomputation Symmetric digit sets for elliptic curve scalar multiplication without precomputation (2014) C. Heuberger, M. Mazzoli Theoretical Computer Science No Publisher selected to publication Analysis of the Binary Asymmetric Joint Sparse Form Analysis of the Binary Asymmetric Joint Sparse Form (2014) C. Heuberger, S. Kropf Combinatorics, Probability and Computing No Publisher selected to publication Canonical trees, compact prefix-free codes and sums of unit fractions: A probabilistic analysis Canonical trees, compact prefix-free codes and sums of unit fractions: A probabilistic analysis (2015) C. Heuberger, D. Krenn, S. Wagner SIAM J. Discrete Math No Publisher selected to publication Asymptotic analysis of the sum of the output of transducers Asymptotic analysis of the sum of the output of transducers (2014) C. Heuberger, S. Kropf, H. Prodinger DMTCS Proceedings No Publisher selected to publication Output Sum of Transducers: Limiting Distribution and Periodic Fluctuation Output Sum of Transducers: Limiting Distribution and Periodic Fluctuation (2015) C. Heuberger, S. Kropf, H. Prodinger Electronic Journal of Combinatorics No Publisher selected to publication Counting Zeros in Random Walks on the Integers and Analysis of Optimal Dual-Pivot Quicksort Counting Zeros in Random Walks on the Integers and Analysis of Optimal Dual-Pivot Quicksort (2016) M. Aumüller, M. Dietzfelbinger, C. Heuberger, D. Krenn, H. Prodinger Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms No Publisher selected to publication Variance and Covariance of Several Simultaneous Outputs of a Markov Chain Variance and Covariance of Several Simultaneous Outputs of a Markov Chain (2016) S. Kropf Discrete Mathematics & Theoretical Computer Science No Publisher selected to publication The height of multiple edge plane trees The height of multiple edge plane trees (2015) C. Heuberger, H. Prodinger, S. Wagner Aequationes mathematicae No Publisher selected to publication Automata in SageMath Automata in SageMath (2016) C. Heuberger, D. Krenn, S. Kropf Discrete Mathematics & Theoretical Computer Science No Publisher selected to publication Analysis of bidirectional ballot sequences and random walks ending in their maximum Analysis of bidirectional ballot sequences and random walks ending in their maximum (2016) B. Hackl, C. Heuberger, H. Prodinger, S. Wagner Annals of Combinatorics No Publisher selected to publication The Register Function and Reductions of Binary Trees and Lattice Paths The Register Function and Reductions of Binary Trees and Lattice Paths (2016) B. Hackl, C. Heuberger, H. Prodinger Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms No Publisher selected to publication Asymptotic Expansions in SageMath Asymptotic Expansions in SageMath (2016) B. Hackl, C. Heuberger, D. Krenn Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms No Publisher selected to publication Analysis of carries in signed digit expansions Analysis of carries in signed digit expansions (2016) C. Heuberger, S. Kropf, H. Prodinger Monatshefte für Mathematik No Publisher selected to publication On the Higher Dimensional Quasi-Power Theorem and a Berry-Esseen Inequality On the Higher Dimensional Quasi-Power Theorem and a Berry-Esseen Inequality (2016) C. Heuberger, S. Kropf Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms No Publisher selected to publication q-Quasiadditive Functions q-Quasiadditive Functions (2016) S. Kropf, S. Wagner Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms No Publisher selected to publication Iterative cutting and pruning of planar trees Iterative cutting and pruning of planar trees (2017) B. Hackl, S. Kropf, H. Prodinger Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO) No Publisher selected to publication Dual-Pivot Quicksort: Optimality, Analysis and Zeros of Associated Lattice Paths Dual-Pivot Quicksort: Optimality, Analysis and Zeros of Associated Lattice Paths (2019) M. Aumüller, M. Dietzfelbinger, C. Heuberger, D. Krenn, H. Prodinger Combinatorics, Probability and Computing No Publisher selected to publication Growing and Destroying Catalan-Stanley Trees Growing and Destroying Catalan-Stanley Trees (2018) B. Hackl, H. Prodinger Discrete Mathematics & Theoretical Computer Science No Publisher selected to publication Fringe analysis of plane trees related to cutting and pruning Fringe analysis of plane trees related to cutting and pruning (2018) B. Hackl, C. Heuberger, S. Kropf, H. Prodinger Aequationes mathematicae No Publisher selected to publication Asymptotic Analysis of Shape Parameters of Trees and Lattice Paths Asymptotic Analysis of Shape Parameters of Trees and Lattice Paths (2018) B. Hackl Hochschulschrift to publication On q-Quasiadditive and q-Quasimultiplicative Functions On q-Quasiadditive and q-Quasimultiplicative Functions (2017) S. Kropf, S. Wagner Electronic Journal of Combinatorics No Publisher selected to publication An extended note on the comparison-optimal dual-pivot quickselect An extended note on the comparison-optimal dual-pivot quickselect (2017) D. Krenn Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO) No Publisher selected to publication Application of Smirnov Words to Waiting Time Distributions of Runs Application of Smirnov Words to Waiting Time Distributions of Runs (2017) U. Freiberg, C. Heuberger, H. Prodinger Electronic Journal of Combinatorics No Publisher selected to publication Higher dimensional quasi-power theorem and Berry–Esseen inequality Higher dimensional quasi-power theorem and Berry–Esseen inequality (2018) C. Heuberger, S. Kropf Monatshefte für Mathematik No Publisher selected to publication Computing J-ideals of a matrix over a principal ideal domain Computing J-ideals of a matrix over a principal ideal domain (2017) C. Heuberger, R. Rissner Linear Algebra and its Applications No Publisher selected to publication Reductions of binary trees and lattice paths induced by the register function Reductions of binary trees and lattice paths induced by the register function (2017) B. Hackl, C. Heuberger, H. Prodinger Theoretical Computer Science No Publisher selected to publication Protection Number in Plane Trees Protection Number in Plane Trees (2017) C. Heuberger, H. Prodinger Applicable Analysis and Discrete Mathematics No Publisher selected to publication On the Monoid Generated by a Lucas Sequence On the Monoid Generated by a Lucas Sequence (2017) C. Heuberger, S. Wagner Number Theory – Diophantine Problems, Uniform Distribution and Applications No Publisher selected to publication Counting ascents in generalized Dyck paths Counting ascents in generalized Dyck paths (2018) B. Hackl, C. Heuberger, H. Prodinger 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018) No Publisher selected to publication
Events	No related events
Lectures	Growing and Cutting down Rooted Plane Trees Growing and Cutting down Rooted Plane Trees B. Hackl Österreich since 11.01.2017 To Lecture Iterative cutting and pruning of planar trees Iterative cutting and pruning of planar trees B. Hackl Österreich since 16.01.2017 To Lecture On the Higher Dimensional Quasi-Power Theorem and a Berry-Esseen Inequality On the Higher Dimensional Quasi-Power Theorem and a Berry-Esseen Inequality C. Heuberger Österreich since 07.07.2016 To Lecture On a Reduction of Lattice Paths On a Reduction of Lattice Paths B. Hackl Österreich since 13.01.2016 To Lecture Analysis of Sequences using Transducer Automata Analysis of Sequences using Transducer Automata C. Heuberger Österreich since 06.09.2016 To Lecture Higher Dimensional Quasi-Power Theorem and Berry–Esseen Inequality Higher Dimensional Quasi-Power Theorem and Berry–Esseen Inequality C. Heuberger Stellenbosch, Südafrika , Österreich since 26.02.2016 To Lecture Die Symbolische Methode, Oder: Wie Funktionen beim Zählen helfen können Die Symbolische Methode, Oder: Wie Funktionen beim Zählen helfen können B. Hackl Österreich since 25.09.2016 To Lecture Distribution of the Number of Factors in Monoids Generated by a Lucas sequence Distribution of the Number of Factors in Monoids Generated by a Lucas sequence C. Heuberger Österreich since 24.10.2016 To Lecture Efficient Scalar Multiplication in Elliptic Curve Cryptography Efficient Scalar Multiplication in Elliptic Curve Cryptography C. Heuberger National Chiao Tung University, Hsinchu, Taiwan , Österreich since 26.09.2016 To Lecture On a Reduction of Lattice Paths On a Reduction of Lattice Paths B. Hackl Österreich since 04.03.2016 To Lecture Non-Adjacent Digit Expansions Non-Adjacent Digit Expansions C. Heuberger Österreich since 03.09.2015 To Lecture Asymptotic analysis of the output sum of transducers Asymptotic analysis of the output sum of transducers S. Kropf Österreich since 25.05.2015 To Lecture Analysis of bidirectional ballot sequences and random walks ending in their maximum Analysis of bidirectional ballot sequences and random walks ending in their maximum C. Heuberger Österreich since 09.06.2015 To Lecture Combinatorial characterization of transducers with bounded variance Combinatorial characterization of transducers with bounded variance S. Kropf Österreich since 12.06.2015 To Lecture Analysis of Carries in Non-Standard Digit Expansions Analysis of Carries in Non-Standard Digit Expansions S. Kropf Österreich since 19.05.2015 To Lecture Analysis of Carries in Non-Standard Digit Expansions Analysis of Carries in Non-Standard Digit Expansions S. Kropf Österreich since 06.05.2015 To Lecture Combinatorial Characterization of Sequences with Bounded Variance Combinatorial Characterization of Sequences with Bounded Variance S. Kropf Österreich since 04.02.2015 To Lecture Scalar Multiplication on Elliptic Curves Using the Binary Asymmetric Joint Sparse Form Scalar Multiplication on Elliptic Curves Using the Binary Asymmetric Joint Sparse Form S. Kropf Österreich since 09.07.2015 To Lecture Automata and analysis of sequences using the SageMath mathematics software system Automata and analysis of sequences using the SageMath mathematics software system C. Heuberger Österreich since 27.05.2015 To Lecture Asymptotic Analysis of the Sum of the Output of Tranducers Asymptotic Analysis of the Sum of the Output of Tranducers S. Kropf Österreich since 11.06.2014 To Lecture Asymptotische Analyse von Ziffernentwicklungen mit Hilfe von Automaten Asymptotische Analyse von Ziffernentwicklungen mit Hilfe von Automaten S. Kropf Österreich since 29.04.2015 To Lecture Combinatorial Characterization of Transducers with Bounded Variance Combinatorial Characterization of Transducers with Bounded Variance S. Kropf Österreich since 18.08.2014 To Lecture Asymptotic analysis of the output sum of transducers Asymptotic analysis of the output sum of transducers S. Kropf Österreich since 19.09.2014 To Lecture Combinatorial Characterization of Transducers with Bounded Variance Combinatorial Characterization of Transducers with Bounded Variance S. Kropf Österreich since 11.07.2014 To Lecture Analysis of Multi-Pivot-Quicksort Analysis of Multi-Pivot-Quicksort C. Heuberger Stellenbosch, South Africa since 22.02.2017 To Lecture Analysis of Sequences using Transducer Automata Analysis of Sequences using Transducer Automata C. Heuberger since 29.11.2017 To Lecture Number of Odd Entries in Pascal's Rhombus and Analysis of k-Regular Sequences Number of Odd Entries in Pascal's Rhombus and Analysis of k-Regular Sequences C. Heuberger since 20.06.2017 To Lecture Growing and Destroying Classes of Plane Trees Growing and Destroying Classes of Plane Trees B. Hackl since 23.06.2017 To Lecture Application of Smirnov Words to Waiting Time Distributions of Runs Application of Smirnov Words to Waiting Time Distributions of Runs C. Heuberger since 18.02.2015 To Lecture