3 Search Results for "Schaller, Ulysse"

Document
DOI: 10.4230/LIPIcs.STACS.2026.11
The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs

Authors: Zylan Benjert, Kostas Lakis, Johannes Lengler, and Raghu Raman Ravi

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We prove that the diameter of threshold (zero temperature) Geometric Inhomogeneous Random Graphs (GIRG) is asymptotically almost surely Θ(log n). This has strong implications for the runtime of many distributed protocols on those graphs, which often have runtimes bounded as a function of the diameter. The GIRG model exhibits many properties empirically found in real-world networks, and the runtime of various practical algorithms has empirically been found to scale in the same way for GIRG and for real-world networks, in particular related to computing distances, diameter, clustering, cliques and chromatic numbers. Thus the GIRG model is a promising candidate for deriving insight about the performance of algorithms in real-world instances. The diameter was previously only known in the one-dimensional case, and the proof relied very heavily on dimension one. Our proof employs a similar Peierls-type argument alongside a novel renormalization scheme. Moreover, instead of using topological arguments (which become complicated in high dimensions) in establishing the connectivity of certain boundaries, we employ some comparatively recent and clearer graph-theoretic machinery. The lower bound is proven via a simple ad-hoc construction.
Cite as

Zylan Benjert, Kostas Lakis, Johannes Lengler, and Raghu Raman Ravi. The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{benjert_et_al:LIPIcs.STACS.2026.11,
  author =	{Benjert, Zylan and Lakis, Kostas and Lengler, Johannes and Ravi, Raghu Raman},
  title =	{{The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.11},
  URN =		{urn:nbn:de:0030-drops-255009},
  doi =		{10.4230/LIPIcs.STACS.2026.11},
  annote =	{Keywords: GIRG, Diameter, Distributed Algorithms, Complex Networks}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.74
Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations

Authors: Bernhard Haeupler, Marc Kaufmann, Raghu Raman Ravi, and Ulysse Schaller

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
This paper presents gossip algorithms for aggregation tasks that demonstrate both robustness to adversarial corruptions of any order of magnitude and optimality across a substantial range of these corruption levels. Gossip algorithms distribute information in a scalable and efficient way by having random pairs of nodes exchange small messages. Value aggregation problems are of particular interest in this setting, as they occur frequently in practice, and many elegant algorithms have been proposed for computing aggregates and statistics such as averages and quantiles. An important and well-studied advantage of gossip algorithms is their robustness to message delays, network churn, and unreliable message transmissions. However, these crucial robustness guarantees only hold if all nodes follow the protocol and no messages are corrupted. In this paper, we remedy this by providing a framework to model both adversarial participants and message corruptions in gossip-style communications by allowing an adversary to control a small fraction of the nodes or corrupt messages arbitrarily. Despite this very powerful and general corruption model, we show that robust gossip algorithms can be designed for many important aggregation problems. Our algorithms guarantee that almost all nodes converge to an approximately correct answer with optimal efficiency and essentially as fast as without corruptions. The design of adversarially-robust gossip algorithms poses completely new challenges. Despite this, our algorithms remain very simple variations of known non-robust algorithms with often only subtle changes to avoid non-compliant nodes gaining too much influence over outcomes. While our algorithms remain simple, their analysis is much more complex and often requires a completely different approach than the non-adversarial setting.
Cite as

Bernhard Haeupler, Marc Kaufmann, Raghu Raman Ravi, and Ulysse Schaller. Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 74:1-74:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{haeupler_et_al:LIPIcs.ITCS.2026.74,
  author =	{Haeupler, Bernhard and Kaufmann, Marc and Ravi, Raghu Raman and Schaller, Ulysse},
  title =	{{Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{74:1--74:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.74},
  URN =		{urn:nbn:de:0030-drops-253611},
  doi =		{10.4230/LIPIcs.ITCS.2026.74},
  annote =	{Keywords: Gossip Algorithms, Distributed Computing, Adversarial Robustness}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.58
The Maximum Label Propagation Algorithm on Sparse Random Graphs

Authors: Charlotte Knierim, Johannes Lengler, Pascal Pfister, Ulysse Schaller, and Angelika Steger

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
In the Maximum Label Propagation Algorithm (Max-LPA), each vertex draws a distinct random label. In each subsequent round, each vertex updates its label to the label that is most frequent among its neighbours (including its own label), breaking ties towards the larger label. It is known that this algorithm can detect communities in random graphs with planted communities if the graphs are very dense, by converging to a different consensus for each community. In [Kothapalli et al., 2013] it was also conjectured that the same result still holds for sparse graphs if the degrees are at least C log n. We disprove this conjecture by showing that even for degrees n^epsilon, for some epsilon>0, the algorithm converges without reaching consensus. In fact, we show that the algorithm does not even reach almost consensus, but converges prematurely resulting in orders of magnitude more communities.
Cite as

Charlotte Knierim, Johannes Lengler, Pascal Pfister, Ulysse Schaller, and Angelika Steger. The Maximum Label Propagation Algorithm on Sparse Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{knierim_et_al:LIPIcs.APPROX-RANDOM.2019.58,
  author =	{Knierim, Charlotte and Lengler, Johannes and Pfister, Pascal and Schaller, Ulysse and Steger, Angelika},
  title =	{{The Maximum Label Propagation Algorithm on Sparse Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{58:1--58:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.58},
  URN =		{urn:nbn:de:0030-drops-112731},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.58},
  annote =	{Keywords: random graphs, distributed algorithms, label propagation algorithms, consensus, community detection}
}
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