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Documents authored by Schaller, Ulysse

Document
DOI: 10.4230/LIPIcs.WG.2026.12
Geometric Routing in Geometric Inhomogeneous Random Graphs

Authors: Yu-Cheng Chiu, Marc Kaufmann, Kostas Lakis, and Ulysse Schaller

Published in: LIPIcs, Volume 376, 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026)

Abstract
We present the first rigorous analysis of decentralized geometric routing in Geometric Inhomogeneous Random Graphs (GIRGs), a weight-agnostic variant of the greedy routing protocol. While greedy routing in GIRGs is known to explain the algorithmic small-world phenomenon by finding ultra-short paths of length Θ(log log n), it assumes additional knowledge of vertex weights beyond geometry, an assumption that is often restrictive or unavailable. We investigate whether the underlying geometry alone is sufficient for efficient navigation. We prove that for power-law weight exponent τ ∈ (2,3) and geometric decay parameter α > τ-1, geometric routing succeeds with constant probability and finds ultra-short paths of length Θ(log log n), matching the optimal asymptotic guarantees for greedy routing. Our analysis further reveals that, upon success, both protocols follow a similar two-phase trajectory, consisting of a rapid ascent to the heavy vertices, followed by efficient navigation to the target. These results demonstrate that, in the appropriate regime, the network’s geometry alone implicitly guides the path to the target through its high-weight core.
Cite as

Yu-Cheng Chiu, Marc Kaufmann, Kostas Lakis, and Ulysse Schaller. Geometric Routing in Geometric Inhomogeneous Random Graphs. In 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 376, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chiu_et_al:LIPIcs.WG.2026.12,
  author =	{Chiu, Yu-Cheng and Kaufmann, Marc and Lakis, Kostas and Schaller, Ulysse},
  title =	{{Geometric Routing in Geometric Inhomogeneous Random Graphs}},
  booktitle =	{52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-430-7},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{376},
  editor =	{Goedgebeur, Jan and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WG.2026.12},
  URN =		{urn:nbn:de:0030-drops-261780},
  doi =		{10.4230/LIPIcs.WG.2026.12},
  annote =	{Keywords: geometric inhomogeneous random graphs (GIRGs), hyperbolic random graphs (HRGs), greedy routing, geometric routing, navigability, small-world phenomenon, decentralized algorithms}
}
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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