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Documents authored by Chazelle, Bernard

Document
DOI: 10.4230/LIPIcs.SAND.2023.10
A Connectivity-Sensitive Approach to Consensus Dynamics

Authors: Bernard Chazelle and Kritkorn Karntikoon

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
The paper resolves a long-standing open question in network dynamics. Averaging-based consensus has long been known to exhibit an exponential gap in relaxation time between the connected and disconnected cases, but a satisfactory explanation has remained elusive. We provide one by deriving nearly tight bounds on the s-energy of disconnected systems. This in turn allows us to relate the convergence rate of consensus dynamics to the number of connected components. We apply our results to opinion formation in social networks and provide a theoretical validation of the concept of an Overton window as an attracting manifold of "viable" opinions.
Cite as

Bernard Chazelle and Kritkorn Karntikoon. A Connectivity-Sensitive Approach to Consensus Dynamics. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chazelle_et_al:LIPIcs.SAND.2023.10,
  author =	{Chazelle, Bernard and Karntikoon, Kritkorn},
  title =	{{A Connectivity-Sensitive Approach to Consensus Dynamics}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.10},
  URN =		{urn:nbn:de:0030-drops-179464},
  doi =		{10.4230/LIPIcs.SAND.2023.10},
  annote =	{Keywords: s-energy, dynamic networks, relaxation time, multiagent systems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.58
Toward a Theory of Markov Influence Systems and their Renormalization

Authors: Bernard Chazelle

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
Nonlinear Markov chains are probabilistic models commonly used in physics, biology, and the social sciences. In "Markov influence systems" (MIS), the transition probabilities of the chains change as a function of the current state distribution. This work introduces a renormalization framework for analyzing the dynamics of MIS. It comes in two independent parts: first, we generalize the standard classification of Markov chain states to the dynamic case by showing how to "parse" graph sequences. We then use this framework to carry out the bifurcation analysis of a few important MIS families. In particular, we show that irreducible MIS are almost always asymptotically periodic. We also give an example of "hyper-torpid" mixing, where a stationary distribution is reached in super-exponential time, a timescale that cannot be achieved by any Markov chain.
Cite as

Bernard Chazelle. Toward a Theory of Markov Influence Systems and their Renormalization. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 58:1-58:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chazelle:LIPIcs.ITCS.2018.58,
  author =	{Chazelle, Bernard},
  title =	{{Toward a Theory of Markov Influence Systems and their Renormalization}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{58:1--58:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.58},
  URN =		{urn:nbn:de:0030-drops-83317},
  doi =		{10.4230/LIPIcs.ITCS.2018.58},
  annote =	{Keywords: Markov influence systems, nonlinear Markov chains, dynamical systems, renormalization, graph sequence parsing}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.17
Self-Sustaining Iterated Learning

Authors: Bernard Chazelle and Chu Wang

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve self-sustainability. Our work is in two parts. First, we characterize iterated learnability in geometric terms and show how a slight, steady increase in the lengths of the training sessions ensures self-sustainability for any discrete language class. In the second part, we tackle the nondiscrete case and investigate self-sustainability for iterated linear regression. We discuss the implications of our findings to issues of non-equilibrium dynamics in natural algorithms.
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Bernard Chazelle and Chu Wang. Self-Sustaining Iterated Learning. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chazelle_et_al:LIPIcs.ITCS.2017.17,
  author =	{Chazelle, Bernard and Wang, Chu},
  title =	{{Self-Sustaining Iterated Learning}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.17},
  URN =		{urn:nbn:de:0030-drops-81711},
  doi =		{10.4230/LIPIcs.ITCS.2017.17},
  annote =	{Keywords: Iterated learning, language evolution, iterated Bayesian linear regression, non-equilibrium dynamics}
}
Document
DOI: 10.4230/DagSemProc.05291.4
Sublinear Geometric Algorithms

Authors: Bernard Chazelle, Ding Liu, and Avner Magen

Published in: Dagstuhl Seminar Proceedings, Volume 5291, Sublinear Algorithms (2006)

Abstract
We present sublinear algorithms to such problems as Detecting of Polytope intersection, Shortest Path on 3D convex Polytopes and volume approximation.
Cite as

Bernard Chazelle, Ding Liu, and Avner Magen. Sublinear Geometric Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 5291, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{chazelle_et_al:DagSemProc.05291.4,
  author =	{Chazelle, Bernard and Liu, Ding and Magen, Avner},
  title =	{{Sublinear Geometric Algorithms}},
  booktitle =	{Sublinear Algorithms},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5291},
  editor =	{Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05291.4},
  URN =		{urn:nbn:de:0030-drops-5548},
  doi =		{10.4230/DagSemProc.05291.4},
  annote =	{Keywords: Sublinear algorithms, computational geometry}
}
Document
DOI: 10.4230/DagSemRep.109
Computational Geometry (Dagstuhl Seminar 9511)

Authors: Helmut Alt, Bernard Chazelle, and Raimund Seidel

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Helmut Alt, Bernard Chazelle, and Raimund Seidel. Computational Geometry (Dagstuhl Seminar 9511). Dagstuhl Seminar Report 109, pp. 1-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1995)

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@TechReport{alt_et_al:DagSemRep.109,
  author =	{Alt, Helmut and Chazelle, Bernard and Seidel, Raimund},
  title =	{{Computational Geometry (Dagstuhl Seminar 9511)}},
  pages =	{1--27},
  ISSN =	{1619-0203},
  year =	{1995},
  type = 	{Dagstuhl Seminar Report},
  number =	{109},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.109},
  URN =		{urn:nbn:de:0030-drops-149970},
  doi =		{10.4230/DagSemRep.109},
}
Document
DOI: 10.4230/DagSemRep.59
Computational Geometry (Dagstuhl Seminar 9312)

Authors: Helmut Alt, Bernard Chazelle, and Emo Welzl

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Helmut Alt, Bernard Chazelle, and Emo Welzl. Computational Geometry (Dagstuhl Seminar 9312). Dagstuhl Seminar Report 59, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1993)

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@TechReport{alt_et_al:DagSemRep.59,
  author =	{Alt, Helmut and Chazelle, Bernard and Welzl, Emo},
  title =	{{Computational Geometry (Dagstuhl Seminar 9312)}},
  pages =	{1--28},
  ISSN =	{1619-0203},
  year =	{1993},
  type = 	{Dagstuhl Seminar Report},
  number =	{59},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.59},
  URN =		{urn:nbn:de:0030-drops-149479},
  doi =		{10.4230/DagSemRep.59},
}
Document
DOI: 10.4230/DagSemRep.22
Computational Geometry (Dagstuhl Seminar 9141)

Authors: Helmut Alt, Bernard Chazelle, and Emo Welzl

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Helmut Alt, Bernard Chazelle, and Emo Welzl. Computational Geometry (Dagstuhl Seminar 9141). Dagstuhl Seminar Report 22, pp. 1-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1991)

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@TechReport{alt_et_al:DagSemRep.22,
  author =	{Alt, Helmut and Chazelle, Bernard and Welzl, Emo},
  title =	{{Computational Geometry (Dagstuhl Seminar 9141)}},
  pages =	{1--27},
  ISSN =	{1619-0203},
  year =	{1991},
  type = 	{Dagstuhl Seminar Report},
  number =	{22},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.22},
  URN =		{urn:nbn:de:0030-drops-149101},
  doi =		{10.4230/DagSemRep.22},
}
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