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Dive into the research topics where Anton Krohmer is active.

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Featured researches published by Anton Krohmer.


international conference on computer communications | 2015

Cliques in hyperbolic random graphs

Tobias Friedrich; Anton Krohmer

Most complex real-world networks display scale-free features. This motivated the study of numerous random graph models with a power-law degree distribution. There is, however, no established and simple model which also has a high clustering of vertices as typically observed in real data. Hyperbolic random graphs bridge this gap. This natural model has recently been introduced by Papadopoulos, Krioukov, Boguna, Vahdat (INFOCOM, pp. 2973–2981, 2010) and has shown theoretically and empirically to fulfill all typical properties of real-world networks, including power-law degree distribution and high clustering. We study cliques in hyperbolic random graphs G and present new results on the expected number of k-cliques E[K k ] and the size of the largest clique ω(G). We observe that there is a phase transition at power-law exponent γ = 3. More precisely, for γ e (2,3) we prove E[K k ] = nk(3-γ)/2 Θ(k)−k and ω(G) = Θ(n(3-γ)/2) while for γ  3 we prove E[K k ] = nΘ(k)−k and ω(G) = Θ(log(n)/log log n). We empirically compare the ω(G) value of several scale-free random graph models with real-world networks. Our experiments show that the ω(G)-predictions by hyperbolic random graphs are much closer to the data than other scale-free random graph models.


international symposium on algorithms and computation | 2012

Parameterized Clique on Scale-Free Networks

Tobias Friedrich; Anton Krohmer

Finding cliques in graphs is a classical problem which is in general NP-hard and parameterized intractable. However, in typical applications like social networks or protein-protein interaction networks, the considered graphs are scale-free, i.e., their degree sequence follows a power law. Their specific structure can be algorithmically exploited and makes it possible to solve clique much more efficiently. We prove that on inhomogeneous random graphs with n nodes and power law exponent γ, cliques of size k can be found in time \(\mathcal{O}(n^2)\) for γ ≥ 3 and in time \(\mathcal{O}(n\, \exp(k^4))\) for 2 < γ < 3.


genetic and evolutionary computation conference | 2012

Efficient algorithms for extracting biological key pathways with global constraints

Jan Baumbach; Tobias Friedrich; Timo Kötzing; Anton Krohmer; Joachim Müller; Josch K. Pauling

The integrated analysis of data of different types and with various interdependencies is one of the major challenges in computational biology. Recently, we developed KeyPathwayMiner, a method that combines biological networks modeled as graphs with disease-specific genetic expression data gained from a set of cases (patients, cell lines, tissues, etc.). We aimed for finding all maximal connected sub-graphs where all nodes but


european symposium on algorithms | 2016

Hyperbolic Random Graphs: Separators and Treewidth

Thomas Bläsius; Tobias Friedrich; Anton Krohmer

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european symposium on research in computer security | 2010

RatFish: a file sharing protocol provably secure against rational users

Michael Backes; Oana Ciobotaru; Anton Krohmer

are expressed in all cases but at most


workshop on algorithms and models for the web graph | 2018

Towards a Systematic Evaluation of Generative Network Models

Thomas Bläsius; Tobias Friedrich; Maximilian Katzmann; Anton Krohmer; Jonathan Striebel

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SIAM Journal on Discrete Mathematics | 2018

On the Diameter of Hyperbolic Random Graphs

Tobias Friedrich; Anton Krohmer

, i.e. key pathways. Thereby, we combined biological networks with OMICS data, instead of analyzing these data sets in isolation. Here we present an alternative approach that avoids a certain bias towards hub nodes: We now aim for extracting all maximal connected sub-networks where all but at most


european symposium on algorithms | 2017

Bounds on the satisfiability threshold for power law distributed random SAT

Tobias Friedrich; Anton Krohmer; Ralf Rothenberger; Thomas Sauerwald; Andrew M. Sutton

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european symposium on algorithms | 2016

Efficient Embedding of Scale-Free Graphs in the Hyperbolic Plane.

Thomas Bläsius; Tobias Friedrich; Anton Krohmer; Sören Laue

nodes are expressed in all cases but in total (!) at most


Integrative Biology | 2012

Efficient key pathway mining: combining networks and OMICS data

Nicolas Alcaraz; Tobias Friedrich; Timo Kötzing; Anton Krohmer; Joachim Müller; Josch Pauling; Jan Baumbach

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Thomas Bläsius

Karlsruhe Institute of Technology

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Timo Kötzing

Hasso Plattner Institute

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Jan Baumbach

University of Southern Denmark

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