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Documents authored by Mazoit, Frédéric

Document
DOI: 10.4230/LIPIcs.STACS.2025.30
Being Efficient in Time, Space, and Workload: a Self-Stabilizing Unison and Its Consequences

Authors: Stéphane Devismes, David Ilcinkas, Colette Johnen, and Frédéric Mazoit

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We present a self-stabilizing algorithm for the unison problem which is efficient in time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works in anonymous asynchronous connected networks in which even local ports are unlabeled. It makes no assumption on the daemon and thus stabilizes under the weakest one: the distributed unfair daemon. In an n-node network of diameter D and assuming the knowledge B ≥ 2D+2, our algorithm only requires Θ(log(B)) bits per node and is fully polynomial as it stabilizes in at most 2D+2 rounds and O(min(n²B, n³)) moves. In particular, it is the first self-stabilizing unison for arbitrary asynchronous anonymous networks achieving an asymptotically optimal stabilization time in rounds using a bounded memory at each node. Furthermore, we show that our solution can be used to efficiently simulate synchronous self-stabilizing algorithms in asynchronous environments. For example, this simulation allows us to design a new state-of-the-art algorithm solving both the leader election and the BFS (Breadth-First Search) spanning tree construction in any identified connected network which, to the best of our knowledge, beats all existing solutions in the literature.
Cite as

Stéphane Devismes, David Ilcinkas, Colette Johnen, and Frédéric Mazoit. Being Efficient in Time, Space, and Workload: a Self-Stabilizing Unison and Its Consequences. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{devismes_et_al:LIPIcs.STACS.2025.30,
  author =	{Devismes, St\'{e}phane and Ilcinkas, David and Johnen, Colette and Mazoit, Fr\'{e}d\'{e}ric},
  title =	{{Being Efficient in Time, Space, and Workload: a Self-Stabilizing Unison and Its Consequences}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{30:1--30:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.30},
  URN =		{urn:nbn:de:0030-drops-228568},
  doi =		{10.4230/LIPIcs.STACS.2025.30},
  annote =	{Keywords: Self-stabilization, unison, time complexity, synchronizer}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.20
Distributed Certification for Classes of Dense Graphs

Authors: Pierre Fraigniaud, Frédéric Mazoit, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
A proof-labeling scheme (PLS) for a boolean predicate Π on labeled graphs is a mechanism used for certifying the legality with respect to Π of global network states in a distributed manner. In a PLS, a certificate is assigned to each processing node of the network, and the nodes are in charge of checking that the collection of certificates forms a global proof that the system is in a correct state, by exchanging the certificates once, between neighbors only. The main measure of complexity is the size of the certificates. Many PLSs have been designed for certifying specific predicates, including cycle-freeness, minimum-weight spanning tree, planarity, etc. In 2021, a breakthrough has been obtained, as a "meta-theorem" stating that a large set of properties have compact PLSs in a large class of networks. Namely, for every MSO₂ property Π on labeled graphs, there exists a PLS for Π with O(log n)-bit certificates for all graphs of bounded tree-depth. This result has been extended to the larger class of graphs with bounded tree-width, using certificates on O(log² n) bits. We extend this result even further, to the larger class of graphs with bounded clique-width, which, as opposed to the other two aforementioned classes, includes dense graphs. We show that, for every MSO₁ property Π on labeled graphs, there exists a PLS for Π with O(log² n)-bit certificates for all graphs of bounded clique-width. As a consequence, certifying families of graphs such as distance-hereditary graphs and (induced) P₄-free graphs (a.k.a., cographs) can be done using a PLS with O(log² n)-bit certificates, merely because each of these two classes can be specified in MSO₁. In fact, we show that certifying P₄-free graphs can be done with certificates on O(log n) bits only. This is in contrast to the class of C₄-free graphs (which does not have bounded clique-width) which requires Ω̃(√n)-bit certificates.
Cite as

Pierre Fraigniaud, Frédéric Mazoit, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca. Distributed Certification for Classes of Dense Graphs. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2023.20,
  author =	{Fraigniaud, Pierre and Mazoit, Fr\'{e}d\'{e}ric and Montealegre, Pedro and Rapaport, Ivan and Todinca, Ioan},
  title =	{{Distributed Certification for Classes of Dense Graphs}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.20},
  URN =		{urn:nbn:de:0030-drops-191467},
  doi =		{10.4230/LIPIcs.DISC.2023.20},
  annote =	{Keywords: CONGEST, Proof Labelling Schemes, clique-width, MSO}
}
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