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Brief Announcement

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

One of the cornerstones of the distributed complexity theory is the derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any randomized LOCAL algorithm that solves a locally checkable labeling problem (LCL) can be derandomized with at most exponential overhead. The original proof assumes that the number of random bits is bounded by some function of the input size. We give a new, simple proof that does not make any such assumptions - it holds even if the randomized algorithm uses infinitely many bits. While at it, we also broaden the scope of the result so that it is directly applicable far beyond LCL problems.

Sameep Dahal, Francesco d'Amore, Henrik Lievonen, Timothé Picavet, and Jukka Suomela. Brief Announcement: Distributed Derandomization Revisited. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 40:1-40:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dahal_et_al:LIPIcs.DISC.2023.40, author = {Dahal, Sameep and d'Amore, Francesco and Lievonen, Henrik and Picavet, Timoth\'{e} and Suomela, Jukka}, title = {{Brief Announcement: Distributed Derandomization Revisited}}, booktitle = {37th International Symposium on Distributed Computing (DISC 2023)}, pages = {40:1--40:5}, 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.2023.40}, URN = {urn:nbn:de:0030-drops-191660}, doi = {10.4230/LIPIcs.DISC.2023.40}, annote = {Keywords: Distributed algorithm, Derandomization, LOCAL model} }

Document

Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the adversary presents the nodes of the input graph one by one, in the same way as in classical online algorithms, but for each node we get to see its radius-T neighborhood before choosing the output. Instead of looking ahead in time, we have the power of looking around in space.
We compare the online-LOCAL model with three other models: the LOCAL model of distributed computing, where each node produces its output based on its radius-T neighborhood, the SLOCAL model, which is the sequential counterpart of LOCAL, and the dynamic-LOCAL model, where changes in the dynamic input graph only influence the radius-T neighborhood of the point of change.
The SLOCAL and dynamic-LOCAL models are sandwiched between the LOCAL and online-LOCAL models. In general, all four models are distinct, but we study in particular locally checkable labeling problems (LCLs), which is a family of graph problems extensively studied in the context of distributed graph algorithms. We prove that for LCL problems in paths, cycles, and rooted trees, all four models are roughly equivalent: the locality of any LCL problem falls in the same broad class - O(log* n), Θ(log n), or n^Θ(1) - in all four models. In particular, this result enables one to generalize prior lower-bound results from the LOCAL model to all four models, and it also allows one to simulate e.g. dynamic-LOCAL algorithms efficiently in the LOCAL model.
We also show that this equivalence does not hold in two-dimensional grids or general bipartite graphs. We provide an online-LOCAL algorithm with locality O(log n) for the 3-coloring problem in bipartite graphs - this is a problem with locality Ω(n^{1/2}) in the LOCAL model and Ω(n^{1/10}) in the SLOCAL model.

Amirreza Akbari, Navid Eslami, Henrik Lievonen, Darya Melnyk, Joona Särkijärvi, and Jukka Suomela. Locality in Online, Dynamic, Sequential, and Distributed Graph Algorithms. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{akbari_et_al:LIPIcs.ICALP.2023.10, author = {Akbari, Amirreza and Eslami, Navid and Lievonen, Henrik and Melnyk, Darya and S\"{a}rkij\"{a}rvi, Joona and Suomela, Jukka}, title = {{Locality in Online, Dynamic, Sequential, and Distributed Graph Algorithms}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {10:1--10:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.10}, URN = {urn:nbn:de:0030-drops-180627}, doi = {10.4230/LIPIcs.ICALP.2023.10}, annote = {Keywords: Online computation, spatial advice, distributed algorithms, computational complexity} }

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

In this paper, we study the notion of mending: given a partial solution to a graph problem, how much effort is needed to take one step towards a proper solution? For example, if we have a partial coloring of a graph, how hard is it to properly color one more node?
In prior work (SIROCCO 2022), this question was formalized and studied from the perspective of mending radius: if there is a hole that we need to patch, how far do we need to modify the solution? In this work, we investigate a complementary notion of mending volume: how many nodes need to be modified to patch a hole?
We focus on the case of locally checkable labeling problems (LCLs) in trees, and show that already in this setting there are two infinite hierarchies of problems: for infinitely many values 0 < α ≤ 1, there is an LCL problem with mending volume Θ(n^α), and for infinitely many values k ≥ 1, there is an LCL problem with mending volume Θ(log^k n). Hence the mendability of LCL problems on trees is a much more fine-grained question than what one would expect based on the mending radius alone.

Darya Melnyk, Jukka Suomela, and Neven Villani. Mending Partial Solutions with Few Changes. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{melnyk_et_al:LIPIcs.OPODIS.2022.21, author = {Melnyk, Darya and Suomela, Jukka and Villani, Neven}, title = {{Mending Partial Solutions with Few Changes}}, booktitle = {26th International Conference on Principles of Distributed Systems (OPODIS 2022)}, pages = {21:1--21:17}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.21}, URN = {urn:nbn:de:0030-drops-176413}, doi = {10.4230/LIPIcs.OPODIS.2022.21}, annote = {Keywords: mending, LCL problems, volume model} }

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**Published in:** LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the [Θ(log n), Θ(n)] region, in two settings. We present one algorithm for unrooted regular trees and another algorithm for rooted regular trees. The algorithms take the description of a locally checkable labeling problem as input, and the running time is polynomial in the size of the problem description. The algorithms decide if the problem is solvable in O(log n) rounds. If not, it is known that the complexity has to be Θ(n^{1/k}) for some k = 1, 2, ..., and in this case the algorithms also output the right value of the exponent k.
In rooted trees in the O(log n) case we can then further determine the exact complexity class by using algorithms from prior work; for unrooted trees the more fine-grained classification in the O(log n) region remains an open question.

Alkida Balliu, Sebastian Brandt, Yi-Jun Chang, Dennis Olivetti, Jan Studený, and Jukka Suomela. Efficient Classification of Locally Checkable Problems in Regular Trees. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2022.8, author = {Balliu, Alkida and Brandt, Sebastian and Chang, Yi-Jun and Olivetti, Dennis and Studen\'{y}, Jan and Suomela, Jukka}, title = {{Efficient Classification of Locally Checkable Problems in Regular Trees}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {8:1--8:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.8}, URN = {urn:nbn:de:0030-drops-171993}, doi = {10.4230/LIPIcs.DISC.2022.8}, annote = {Keywords: locally checkable labeling, locality, distributed computational complexity} }

Document

Brief Announcement

**Published in:** LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Online algorithms make decisions based on past inputs, with the goal of being competitive against an algorithm that sees also future inputs. In this work, we introduce time-local online algorithms; these are online algorithms in which the output at any given time is a function of only T latest inputs. Our main observation is that time-local online algorithms are closely connected to local distributed graph algorithms: distributed algorithms make decisions based on the local information in the spatial dimension, while time-local online algorithms make decisions based on the local information in the temporal dimension. We formalize this connection, and show how we can directly use the tools developed to study distributed approximability of graph optimization problems to prove upper and lower bounds on the competitive ratio achieved with time-local online algorithms. Moreover, we show how to use computational techniques to synthesize optimal time-local algorithms.

Maciej Pacut, Mahmoud Parham, Joel Rybicki, Stefan Schmid, Jukka Suomela, and Aleksandr Tereshchenko. Brief Announcement: Temporal Locality in Online Algorithms. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 52:1-52:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{pacut_et_al:LIPIcs.DISC.2022.52, author = {Pacut, Maciej and Parham, Mahmoud and Rybicki, Joel and Schmid, Stefan and Suomela, Jukka and Tereshchenko, Aleksandr}, title = {{Brief Announcement: Temporal Locality in Online Algorithms}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {52:1--52:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.52}, URN = {urn:nbn:de:0030-drops-172431}, doi = {10.4230/LIPIcs.DISC.2022.52}, annote = {Keywords: Online algorithms, distributed algorithms} }

Document

**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for non-LCL problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in O(log n) rounds in the LOCAL model, but requires Ω̃(n^{1/2}) rounds in the CONGEST model.

Alkida Balliu, Keren Censor-Hillel, Yannic Maus, Dennis Olivetti, and Jukka Suomela. Locally Checkable Labelings with Small Messages. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2021.8, author = {Balliu, Alkida and Censor-Hillel, Keren and Maus, Yannic and Olivetti, Dennis and Suomela, Jukka}, title = {{Locally Checkable Labelings with Small Messages}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {8:1--8:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.8}, URN = {urn:nbn:de:0030-drops-148109}, doi = {10.4230/LIPIcs.DISC.2021.8}, annote = {Keywords: distributed graph algorithms, CONGEST, locally checkable labelings} }

Document

Brief Announcement

**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

We show that any algorithm that solves the sinkless orientation problem in the supported LOCAL model requires Ω(log n) rounds, and this is tight. The supported LOCAL is at least as strong as the usual LOCAL model, and as a corollary this also gives a new, short and elementary proof that shows that the round complexity of the sinkless orientation problem in the deterministic LOCAL model is Ω(log n).

Janne H. Korhonen, Ami Paz, Joel Rybicki, Stefan Schmid, and Jukka Suomela. Brief Announcement: Sinkless Orientation Is Hard Also in the Supported LOCAL Model. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 58:1-58:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{korhonen_et_al:LIPIcs.DISC.2021.58, author = {Korhonen, Janne H. and Paz, Ami and Rybicki, Joel and Schmid, Stefan and Suomela, Jukka}, title = {{Brief Announcement: Sinkless Orientation Is Hard Also in the Supported LOCAL Model}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {58:1--58:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.58}, URN = {urn:nbn:de:0030-drops-148609}, doi = {10.4230/LIPIcs.DISC.2021.58}, annote = {Keywords: Supported LOCAL model, sinkless orientation, round elimination} }

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Invited Talk

**Published in:** LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Computer scientists seek to understand what can be automated, but what do we know about automating our own work? Can we outsource our own research questions to computers? In this talk I will discuss this question from the perspective of the theory of distributed computing. I will present not only recent examples of human-computer-collaborations that have resulted in major breakthroughs in our understanding of distributed computing, but I will also explore the fundamental limits of such approaches.

Jukka Suomela. Can We Automate Our Own Work - or Show That It Is Hard? (Invited Talk). In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{suomela:LIPIcs.OPODIS.2020.3, author = {Suomela, Jukka}, title = {{Can We Automate Our Own Work - or Show That It Is Hard?}}, booktitle = {24th International Conference on Principles of Distributed Systems (OPODIS 2020)}, pages = {3:1--3:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-176-4}, ISSN = {1868-8969}, year = {2021}, volume = {184}, editor = {Bramas, Quentin and Oshman, Rotem and Romano, Paolo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.3}, URN = {urn:nbn:de:0030-drops-134881}, doi = {10.4230/LIPIcs.OPODIS.2020.3}, annote = {Keywords: Distributed Computing} }

Document

**Published in:** LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two in the edge labeling formalism. Examples of binary labeling problems include sinkless orientation, sinkless and sourceless orientation, 2-vertex coloring, perfect matching, and the task of coloring edges red and blue such that all nodes are incident to at least one red and at least one blue edge. More generally, we can encode e.g. any cardinality constraints on indegrees and outdegrees.
We study the deterministic time complexity of solving a given binary labeling problem in trees, in the usual LOCAL model of distributed computing. We show that the complexity of any such problem is in one of the following classes: O(1), Θ(log n), Θ(n), or unsolvable. In particular, a problem that can be represented in the binary labeling formalism cannot have time complexity Θ(log^* n), and hence we know that e.g. any encoding of maximal matchings has to use at least three labels (which is tight).
Furthermore, given the description of any binary labeling problem, we can easily determine in which of the four classes it is and what is an asymptotically optimal algorithm for solving it. Hence the distributed time complexity of binary labeling problems is decidable, not only in principle, but also in practice: there is a simple and efficient algorithm that takes the description of a binary labeling problem and outputs its distributed time complexity.

Alkida Balliu, Sebastian Brandt, Yuval Efron, Juho Hirvonen, Yannic Maus, Dennis Olivetti, and Jukka Suomela. Classification of Distributed Binary Labeling Problems. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2020.17, author = {Balliu, Alkida and Brandt, Sebastian and Efron, Yuval and Hirvonen, Juho and Maus, Yannic and Olivetti, Dennis and Suomela, Jukka}, title = {{Classification of Distributed Binary Labeling Problems}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {17:1--17:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-168-9}, ISSN = {1868-8969}, year = {2020}, volume = {179}, editor = {Attiya, Hagit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.17}, URN = {urn:nbn:de:0030-drops-130957}, doi = {10.4230/LIPIcs.DISC.2020.17}, annote = {Keywords: LOCAL model, graph problems, locally checkable labeling problems, distributed computational complexity} }

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Brief Announcement

**Published in:** LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for the stable orientation problem, which is a special case of the more general locally optimal semi-matching problem. The prior work by Czygrinow et al. (DISC 2012) finds a locally optimal semi-matching in O(Δ⁵) rounds in graphs of maximum degree Δ, which directly implies an algorithm with the same runtime for stable orientations. We improve the runtime to O(Δ⁴) for stable orientations and prove a lower bound of Ω(Δ) rounds.

Sebastian Brandt, Barbara Keller, Joel Rybicki, Jukka Suomela, and Jara Uitto. Brief Announcement: Efficient Load-Balancing Through Distributed Token Dropping. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 40:1-40:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brandt_et_al:LIPIcs.DISC.2020.40, author = {Brandt, Sebastian and Keller, Barbara and Rybicki, Joel and Suomela, Jukka and Uitto, Jara}, title = {{Brief Announcement: Efficient Load-Balancing Through Distributed Token Dropping}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {40:1--40:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-168-9}, ISSN = {1868-8969}, year = {2020}, volume = {179}, editor = {Attiya, Hagit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.40}, URN = {urn:nbn:de:0030-drops-131182}, doi = {10.4230/LIPIcs.DISC.2020.40}, annote = {Keywords: distributed algorithms, graph problems, semi-matching} }

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Brief Announcement

**Published in:** LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

We study the following algorithm synthesis question: given the description of a locally checkable graph problem Π for paths or cycles, determine in which instances Π is solvable, determine what is the locality of Π, and construct an asymptotically optimal distributed algorithm for solving Π (in the usual LOCAL model of distributed computing). To answer such questions, we represent Π as a nondeterministic finite automaton ℳ over a unary alphabet, and identify polynomial-time-computable properties of automaton ℳ that capture the locality and solvability of problem Π.

Yi-Jun Chang, Jan Studený, and Jukka Suomela. Brief Announcement: Distributed Graph Problems Through an Automata-Theoretic Lens. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 41:1-41:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chang_et_al:LIPIcs.DISC.2020.41, author = {Chang, Yi-Jun and Studen\'{y}, Jan and Suomela, Jukka}, title = {{Brief Announcement: Distributed Graph Problems Through an Automata-Theoretic Lens}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {41:1--41:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-168-9}, ISSN = {1868-8969}, year = {2020}, volume = {179}, editor = {Attiya, Hagit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.41}, URN = {urn:nbn:de:0030-drops-131197}, doi = {10.4230/LIPIcs.DISC.2020.41}, annote = {Keywords: Algorithm synthesis, locally checkable labeling problems, LOCAL model, locality, distributed computational complexity, nondeterministic finite automata} }

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Invited Talk

**Published in:** LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

The theory of distributed computing aims at understanding which tasks can be solved efficiently in large distributed systems. This forms the basis for our understanding of the modern world, which heavily depends on world-wide communication networks and large-scale distributed computer systems.
In distributed computing the key computational resource is communication, and we seek to find out which computational problems can be solved with only a few communication steps. This is directly connected to the concept of locality: in T synchronous communication rounds, all nodes in a network can gather all information in their radius-T neighborhoods, but not any further. Hence the distributed time complexity of a graph problem can be defined in two equivalent ways: it is the number of communication rounds needed to solve the problem, and it is the distance up to which individual nodes need to see in order to choose their own part of the solution.
While the locality of graph problems has been studied already since the 1980s, only in the past four years we have started to take big leaps in understanding what the landscape of distributed time complexity looks like and with what kind of tools and techniques we can study it.
One concept that has been a driving force in the recent developments is the notion of locally verifiable problems. These are graph problems in which a solution is feasible if and only if it looks valid in all constant-radius neighborhoods; put otherwise, these are problems that could be solved efficiently with a nondeterministic distributed algorithm, and hence they form a natural distributed analogue of class NP. Now the key question is this: if a problem is locally verifiable, is it also locally solvable, and if not, what can we say about its distributed time complexity?
Naor and Stockmeyer [SIAM J. Comput. 1995] formalized the idea of locally verifiable problems by introducing the class of LCL problems (locally checkable labeling problems). While the concept is old, and over the years we have seen results related to the locality of many specific LCLs, little was known about the distributed complexity of LCLs in general. By 2015, we had only seen examples of LCLs with localities O(1), Θ(log^* n), and Θ(n), and it was wide open whether these three classes are all that there is.
All this started to change rapidly after we proved [Brandt et al., STOC 2016] that there are natural examples of LCLs that have a locality strictly between ω(log^* n) and o(n). The same paper also paved the way for the development of a new general-purpose proof technique for analyzing the locality of locally verifiable problems, namely round elimination.
Now after four years of work and a number of papers by several research teams working in the area, we have reached a point in which there is a near-complete picture of the landscape of LCL problems - and it looks nothing like what we would have expected.

Jukka Suomela. Landscape of Locality (Invited Talk). In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{suomela:LIPIcs.SWAT.2020.2, author = {Suomela, Jukka}, title = {{Landscape of Locality}}, booktitle = {17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)}, pages = {2:1--2:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-150-4}, ISSN = {1868-8969}, year = {2020}, volume = {162}, editor = {Albers, Susanne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.2}, URN = {urn:nbn:de:0030-drops-122490}, doi = {10.4230/LIPIcs.SWAT.2020.2}, annote = {Keywords: Theory of distributed computing, Network algorithms, Locality, Distributed time complexity} }

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Complete Volume

**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

LIPIcs, Volume 146, DISC'19, Complete Volume

33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{suomela:LIPIcs.DISC.2019, title = {{LIPIcs, Volume 146, DISC'19, Complete Volume}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019}, URN = {urn:nbn:de:0030-drops-113878}, doi = {10.4230/LIPIcs.DISC.2019}, annote = {Keywords: Software and its engineering, Distributed systems organizing principles; Computing methodologies, Distributed computing methodologies} }

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Front Matter

**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Front Matter, Table of Contents, Preface, Conference Organization

33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{suomela:LIPIcs.DISC.2019.0, author = {Suomela, Jukka}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {0:i--0:xviii}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.0}, URN = {urn:nbn:de:0030-drops-113074}, doi = {10.4230/LIPIcs.DISC.2019.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

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**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

The landscape of the distributed time complexity is nowadays well-understood for subpolynomial complexities. When we look at deterministic algorithms in the LOCAL model and locally checkable problems (LCLs) in bounded-degree graphs, the following picture emerges:
- There are lots of problems with time complexities Theta(log^* n) or Theta(log n).
- It is not possible to have a problem with complexity between omega(log^* n) and o(log n).
- In general graphs, we can construct LCL problems with infinitely many complexities between omega(log n) and n^{o(1)}.
- In trees, problems with such complexities do not exist.
However, the high end of the complexity spectrum was left open by prior work. In general graphs there are problems with complexities of the form Theta(n^alpha) for any rational 0 < alpha <=1/2, while for trees only complexities of the form Theta(n^{1/k}) are known. No LCL problem with complexity between omega(sqrt{n}) and o(n) is known, and neither are there results that would show that such problems do not exist. We show that:
- In general graphs, we can construct LCL problems with infinitely many complexities between omega(sqrt{n}) and o(n).
- In trees, problems with such complexities do not exist.
Put otherwise, we show that any LCL with a complexity o(n) can be solved in time O(sqrt{n}) in trees, while the same is not true in general graphs.

Alkida Balliu, Sebastian Brandt, Dennis Olivetti, and Jukka Suomela. Almost Global Problems in the LOCAL Model. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2018.9, author = {Balliu, Alkida and Brandt, Sebastian and Olivetti, Dennis and Suomela, Jukka}, title = {{Almost Global Problems in the LOCAL Model}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {9:1--9:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.9}, URN = {urn:nbn:de:0030-drops-97982}, doi = {10.4230/LIPIcs.DISC.2018.9}, annote = {Keywords: Distributed complexity theory, locally checkable labellings, LOCAL model} }

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**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Given two colorings of a graph, we consider the following problem: can we recolor the graph from one coloring to the other through a series of elementary changes, such that the graph is properly colored after each step?
We introduce the notion of distributed recoloring: The input graph represents a network of computers that needs to be recolored. Initially, each node is aware of its own input color and target color. The nodes can exchange messages with each other, and eventually each node has to stop and output its own recoloring schedule, indicating when and how the node changes its color. The recoloring schedules have to be globally consistent so that the graph remains properly colored at each point, and we require that adjacent nodes do not change their colors simultaneously.
We are interested in the following questions: How many communication rounds are needed (in the deterministic LOCAL model of distributed computing) to find a recoloring schedule? What is the length of the recoloring schedule? And how does the picture change if we can use extra colors to make recoloring easier?
The main contributions of this work are related to distributed recoloring with one extra color in the following graph classes: trees, 3-regular graphs, and toroidal grids.

Marthe Bonamy, Paul Ouvrard, Mikaël Rabie, Jukka Suomela, and Jara Uitto. Distributed Recoloring. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bonamy_et_al:LIPIcs.DISC.2018.12, author = {Bonamy, Marthe and Ouvrard, Paul and Rabie, Mika\"{e}l and Suomela, Jukka and Uitto, Jara}, title = {{Distributed Recoloring}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {12:1--12:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.12}, URN = {urn:nbn:de:0030-drops-98012}, doi = {10.4230/LIPIcs.DISC.2018.12}, annote = {Keywords: Distributed Systems, Graph Algorithms, Local Computations} }

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**Published in:** OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)

We study a combinatorial optimization problem that is motivated by the scenario of autonomous cars driving on a multi-lane highway: some cars need to change lanes before the next intersection, and if there is congestion, cars need to slow down to make space for those who are changing lanes. There are two natural objective functions to minimize: (1) how long does it take for all traffic to clear the road, and (2) the total number of maneuvers. In this work, we present an approximation algorithm for solving these problems in the two-lane case and a hardness result for the multi-lane case.

Thomas Petig, Elad M. Schiller, and Jukka Suomela. Changing Lanes on a Highway. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{petig_et_al:OASIcs.ATMOS.2018.9, author = {Petig, Thomas and Schiller, Elad M. and Suomela, Jukka}, title = {{Changing Lanes on a Highway}}, booktitle = {18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)}, pages = {9:1--9:15}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-096-5}, ISSN = {2190-6807}, year = {2018}, volume = {65}, editor = {Bornd\"{o}rfer, Ralf and Storandt, Sabine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.9}, URN = {urn:nbn:de:0030-drops-97148}, doi = {10.4230/OASIcs.ATMOS.2018.9}, annote = {Keywords: Collaborative agents, vehicle scheduling, traffic optimization, approximation algorithms} }

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**Published in:** LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017)

While the relationship of time and space is an established topic in traditional centralised com- plexity theory, this is not the case in distributed computing. We aim to remedy this by studying the time and space complexity of algorithms in a weak message-passing model of distributed com- puting. While a constant number of communication rounds implies a constant number of states visited during the execution, the other direction is not clear at all. We show that indeed, there exist non-trivial graph problems that are solvable by constant-space algorithms but that require a non-constant running time. Somewhat surprisingly, this holds even when restricted to the class of only cycle and path graphs. Our work provides us with a new complexity class for distributed computing and raises interesting questions about the existence of further combinations of time and space complexity.

Tuomo Lempiäinen and Jukka Suomela. Constant Space and Non-Constant Time in Distributed Computing. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{lempiainen_et_al:LIPIcs.OPODIS.2017.30, author = {Lempi\"{a}inen, Tuomo and Suomela, Jukka}, title = {{Constant Space and Non-Constant Time in Distributed Computing}}, booktitle = {21st International Conference on Principles of Distributed Systems (OPODIS 2017)}, pages = {30:1--30:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-061-3}, ISSN = {1868-8969}, year = {2018}, volume = {95}, editor = {Aspnes, James and Bessani, Alysson and Felber, Pascal and Leit\~{a}o, Jo\~{a}o}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.30}, URN = {urn:nbn:de:0030-drops-86368}, doi = {10.4230/LIPIcs.OPODIS.2017.30}, annote = {Keywords: distributed computing, space complexity, constant-space algorithms, weak models, Thue-Morse sequence} }

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**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires orienting the edges such that each node has almost the same number of incoming and outgoing edges, again up to a small additive discrepancy.
We present deterministic distributed algorithms for both variants, which improve on their counterparts presented by Ghaffari and Su [SODA'17]: our algorithms are significantly simpler and faster, and have a much smaller discrepancy. This also leads to a faster and simpler deterministic algorithm for (2+o(1))Delta-edge-coloring, improving on that of Ghaffari and Su.

Mohsen Ghaffari, Juho Hirvonen, Fabian Kuhn, Yannic Maus, Jukka Suomela, and Jara Uitto. Improved Distributed Degree Splitting and Edge Coloring. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ghaffari_et_al:LIPIcs.DISC.2017.19, author = {Ghaffari, Mohsen and Hirvonen, Juho and Kuhn, Fabian and Maus, Yannic and Suomela, Jukka and Uitto, Jara}, title = {{Improved Distributed Degree Splitting and Edge Coloring}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {19:1--19:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.19}, URN = {urn:nbn:de:0030-drops-79794}, doi = {10.4230/LIPIcs.DISC.2017.19}, annote = {Keywords: Distributed Graph Algorithms, Degree Splitting, Edge Coloring, Discrepancy} }

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Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of lower bounds for the congested clique; indeed, it is now know that proving explicit congested clique lower bounds is as difficult as proving circuit lower bounds. In this work, we use traditional complexity-theoretic tools to build a clearer picture of the complexity landscape of the congested clique, proving non-constructive lower bounds and studying the relationships between natural problems.

Janne H. Korhonen and Jukka Suomela. Brief Announcement: Towards a Complexity Theory for the Congested Clique. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 55:1-55:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{korhonen_et_al:LIPIcs.DISC.2017.55, author = {Korhonen, Janne H. and Suomela, Jukka}, title = {{Brief Announcement: Towards a Complexity Theory for the Congested Clique}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {55:1--55:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.55}, URN = {urn:nbn:de:0030-drops-79889}, doi = {10.4230/LIPIcs.DISC.2017.55}, annote = {Keywords: distributed computing, congested clique, complexity theory} }

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**Published in:** LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Given n colored balls, we want to detect if more than n/2 of them have the same color, and if so find one ball with such majority color. We are only allowed to choose two balls and compare their colors, and the goal is to minimize the total number of such operations. A well-known exercise is to show how to find such a ball with only 2n comparisons while using only a logarithmic number of bits for bookkeeping. The resulting algorithm is called the Boyer-Moore majority vote algorithm. It is known that any deterministic method needs 3n/2-2 comparisons in the worst case, and this is tight. However, it is not clear what is the required number of comparisons if we allow randomization. We construct a randomized algorithm which always correctly finds a ball of the majority color (or detects that there is none) using, with high probability, only 7n/6+o(n) comparisons. We also prove that the expected number of comparisons used by any such randomized method is at least 1.019n.

Pawel Gawrychowski, Jukka Suomela, and Przemyslaw Uznanski. Randomized Algorithms for Finding a Majority Element. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{gawrychowski_et_al:LIPIcs.SWAT.2016.9, author = {Gawrychowski, Pawel and Suomela, Jukka and Uznanski, Przemyslaw}, title = {{Randomized Algorithms for Finding a Majority Element}}, booktitle = {15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)}, pages = {9:1--9:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-011-8}, ISSN = {1868-8969}, year = {2016}, volume = {53}, editor = {Pagh, Rasmus}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.9}, URN = {urn:nbn:de:0030-drops-60273}, doi = {10.4230/LIPIcs.SWAT.2016.9}, annote = {Keywords: majority, randomized algorithms, lower bounds} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 9371, Algorithmic Methods for Distributed Cooperative Systems (2010)

An introduction to distributed algorithms, in particular local algorithms. Essentially a practice talk of my SSS 2009 invited talk.

Christoph Lenzen, Jukka Suomela, and Roger Wattenhofer. Local Algorithms: Self-Stabilization on Speed. In Algorithmic Methods for Distributed Cooperative Systems. Dagstuhl Seminar Proceedings, Volume 9371, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{lenzen_et_al:DagSemProc.09371.3, author = {Lenzen, Christoph and Suomela, Jukka and Wattenhofer, Roger}, title = {{Local Algorithms: Self-Stabilization on Speed}}, booktitle = {Algorithmic Methods for Distributed Cooperative Systems}, pages = {1--18}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2010}, volume = {9371}, editor = {S\'{a}ndor Fekete and Stefan Fischer and Martin Riedmiller and Suri Subhash}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09371.3}, URN = {urn:nbn:de:0030-drops-24257}, doi = {10.4230/DagSemProc.09371.3}, annote = {Keywords: Local Algorithms, Self-Stabilization, Lower Bounds, Upper Bounds, MIS} }

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