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Documents authored by Hahn-Klimroth, Max

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.54
The Full Rank Condition for Sparse Random Matrices

Authors: Amin Coja-Oghlan, Jane Gao, Max Hahn-Klimroth, Joon Lee, Noela Müller, and Maurice Rolvien

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

Abstract
We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. Inspired by low-density parity check codes, the family of random matrices that we investigate is very general and encompasses both matrices over finite fields and {0,1}-matrices over the rationals. The proof combines statistical physics-inspired coupling techniques with local limit arguments.
Cite as

Amin Coja-Oghlan, Jane Gao, Max Hahn-Klimroth, Joon Lee, Noela Müller, and Maurice Rolvien. The Full Rank Condition for Sparse Random Matrices. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 54:1-54:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cojaoghlan_et_al:LIPIcs.APPROX/RANDOM.2023.54,
  author =	{Coja-Oghlan, Amin and Gao, Jane and Hahn-Klimroth, Max and Lee, Joon and M\"{u}ller, Noela and Rolvien, Maurice},
  title =	{{The Full Rank Condition for Sparse Random Matrices}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{54:1--54:14},
  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.2023.54},
  URN =		{urn:nbn:de:0030-drops-188792},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.54},
  annote =	{Keywords: random matrices, rank, finite fields, rationals}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2022.23
On the Hierarchy of Distributed Majority Protocols

Authors: Petra Berenbrink, Amin Coja-Oghlan, Oliver Gebhard, Max Hahn-Klimroth, Dominik Kaaser, and Malin Rau

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract
We study the consensus problem among n agents, defined as follows. Initially, each agent holds one of two possible opinions. The goal is to reach a consensus configuration in which every agent shares the same opinion. To this end, agents randomly sample other agents and update their opinion according to a simple update function depending on the sampled opinions. We consider two communication models: the gossip model and a variant of the population model. In the gossip model, agents are activated in parallel, synchronous rounds. In the population model, one agent is activated after the other in a sequence of discrete time steps. For both models we analyze the following natural family of majority processes called j-Majority: when activated, every agent samples j other agents uniformly at random (with replacement) and adopts the majority opinion among the sample (breaking ties uniformly at random). As our main result we show a hierarchy among majority protocols: (j+1)-Majority (for j > 1) converges stochastically faster than j-Majority for any initial opinion configuration. In our analysis we use Strassen’s Theorem to prove the existence of a coupling. This gives an affirmative answer for the case of two opinions to an open question asked by Berenbrink et al. [PODC 2017].
Cite as

Petra Berenbrink, Amin Coja-Oghlan, Oliver Gebhard, Max Hahn-Klimroth, Dominik Kaaser, and Malin Rau. On the Hierarchy of Distributed Majority Protocols. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{berenbrink_et_al:LIPIcs.OPODIS.2022.23,
  author =	{Berenbrink, Petra and Coja-Oghlan, Amin and Gebhard, Oliver and Hahn-Klimroth, Max and Kaaser, Dominik and Rau, Malin},
  title =	{{On the Hierarchy of Distributed Majority Protocols}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.23},
  URN =		{urn:nbn:de:0030-drops-176434},
  doi =		{10.4230/LIPIcs.OPODIS.2022.23},
  annote =	{Keywords: Consensus, Majority, Hierarchy, Stochastic Dominance, Population Protocols, Gossip Model, Strassen’s Theorem}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.8
Efficient and Accurate Group Testing via Belief Propagation: An Empirical Study

Authors: Amin Coja-Oghlan, Max Hahn-Klimroth, Philipp Loick, and Manuel Penschuck

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
The group testing problem asks for efficient pooling schemes and inference algorithms that allow to screen moderately large numbers of samples for rare infections. The goal is to accurately identify the infected individuals while minimizing the number of tests. We propose the novel adaptive pooling scheme adaptive Belief Propagation (ABP) that acknowledges practical limitations such as limited pooling sizes and noisy tests that may give imperfect answers. We demonstrate that the accuracy of ABP surpasses that of individual testing despite using few overall tests. The new design comes with Belief Propagation as an efficient inference algorithm. While the development of ABP is guided by mathematical analyses and asymptotic insights, we conduct an experimental study to obtain results on practical population sizes.
Cite as

Amin Coja-Oghlan, Max Hahn-Klimroth, Philipp Loick, and Manuel Penschuck. Efficient and Accurate Group Testing via Belief Propagation: An Empirical Study. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cojaoghlan_et_al:LIPIcs.SEA.2022.8,
  author =	{Coja-Oghlan, Amin and Hahn-Klimroth, Max and Loick, Philipp and Penschuck, Manuel},
  title =	{{Efficient and Accurate Group Testing via Belief Propagation: An Empirical Study}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.8},
  URN =		{urn:nbn:de:0030-drops-165422},
  doi =		{10.4230/LIPIcs.SEA.2022.8},
  annote =	{Keywords: Group testing, Probabilistic Construction, Belief Propagation, Simulation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.24
Inference and Mutual Information on Random Factor Graphs

Authors: Amin Coja-Oghlan, Max Hahn-Klimroth, Philipp Loick, Noela Müller, Konstantinos Panagiotou, and Matija Pasch

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
Random factor graphs provide a powerful framework for the study of inference problems such as decoding problems or the stochastic block model. Information-theoretically the key quantity of interest is the mutual information between the observed factor graph and the underlying ground truth around which the factor graph was created; in the stochastic block model, this would be the planted partition. The mutual information gauges whether and how well the ground truth can be inferred from the observable data. For a very general model of random factor graphs we verify a formula for the mutual information predicted by physics techniques. As an application we prove a conjecture about low-density generator matrix codes from [Montanari: IEEE Transactions on Information Theory 2005]. Further applications include phase transitions of the stochastic block model and the mixed k-spin model from physics.
Cite as

Amin Coja-Oghlan, Max Hahn-Klimroth, Philipp Loick, Noela Müller, Konstantinos Panagiotou, and Matija Pasch. Inference and Mutual Information on Random Factor Graphs. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cojaoghlan_et_al:LIPIcs.STACS.2021.24,
  author =	{Coja-Oghlan, Amin and Hahn-Klimroth, Max and Loick, Philipp and M\"{u}ller, Noela and Panagiotou, Konstantinos and Pasch, Matija},
  title =	{{Inference and Mutual Information on Random Factor Graphs}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.24},
  URN =		{urn:nbn:de:0030-drops-136692},
  doi =		{10.4230/LIPIcs.STACS.2021.24},
  annote =	{Keywords: Information theory, random factor graphs, inference problems, phase transitions}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.43
Information-Theoretic and Algorithmic Thresholds for Group Testing

Authors: Amin Coja-Oghlan, Oliver Gebhard, Max Hahn-Klimroth, and Philipp Loick

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff at least one individual in the group is infected. With all tests conducted in parallel, what is the least number of tests required to identify the status of all individuals? In a recent test design [Aldridge et al. 2016] the individuals are assigned to test groups randomly, with every individual joining an equal number of groups. We pinpoint the sharp threshold for the number of tests required in this randomised design so that it is information-theoretically possible to infer the infection status of every individual. Moreover, we analyse two efficient inference algorithms. These results settle conjectures from [Aldridge et al. 2014, Johnson et al. 2019].
Cite as

Amin Coja-Oghlan, Oliver Gebhard, Max Hahn-Klimroth, and Philipp Loick. Information-Theoretic and Algorithmic Thresholds for Group Testing. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cojaoghlan_et_al:LIPIcs.ICALP.2019.43,
  author =	{Coja-Oghlan, Amin and Gebhard, Oliver and Hahn-Klimroth, Max and Loick, Philipp},
  title =	{{Information-Theoretic and Algorithmic Thresholds for Group Testing}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.43},
  URN =		{urn:nbn:de:0030-drops-106196},
  doi =		{10.4230/LIPIcs.ICALP.2019.43},
  annote =	{Keywords: Group testing problem, phase transitions, information theory, efficient algorithms, sharp threshold, Bayesian inference}
}
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