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

We show the first conditionally optimal deterministic algorithm for 3-coloring forests in the low-space massively parallel computation (MPC) model. Our algorithm runs in O(log log n) rounds and uses optimal global space. The best previous algorithm requires 4 colors [Ghaffari, Grunau, Jin, DISC'20] and is randomized, while our algorithm are inherently deterministic.
Our main technical contribution is an O(log log n)-round algorithm to compute a partition of the forest into O(log n) ordered layers such that every node has at most two neighbors in the same or higher layers. Similar decompositions are often used in the area and we believe that this result is of independent interest. Our results also immediately yield conditionally optimal deterministic algorithms for maximal independent set and maximal matching for forests, matching the state of the art [Giliberti, Fischer, Grunau, SPAA'23]. In contrast to their solution, our algorithms are not based on derandomization, and are arguably simpler.

Christoph Grunau, Rustam Latypov, Yannic Maus, Shreyas Pai, and Jara Uitto. Conditionally Optimal Parallel Coloring of Forests. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{grunau_et_al:LIPIcs.DISC.2023.23, author = {Grunau, Christoph and Latypov, Rustam and Maus, Yannic and Pai, Shreyas and Uitto, Jara}, title = {{Conditionally Optimal Parallel Coloring of Forests}}, booktitle = {37th International Symposium on Distributed Computing (DISC 2023)}, pages = {23:1--23:20}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.23}, URN = {urn:nbn:de:0030-drops-191494}, doi = {10.4230/LIPIcs.DISC.2023.23}, annote = {Keywords: massively parallel computation, coloring, forests, optimal} }

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**Published in:** LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of the rotations of all vertices and crossings. A drawing is simple if each pair of edges has at most one common point. Gioan’s Theorem states that for any two simple drawings of the complete graph K_n with the same crossing edge pairs, one drawing can be transformed into the other by a sequence of triangle flips (a.k.a. Reidemeister moves of Type 3). This operation refers to the act of moving one edge of a triangular cell formed by three pairwise crossing edges over the opposite crossing of the cell, via a local transformation.
We investigate to what extent Gioan-type theorems can be obtained for wider classes of graphs. A necessary (but in general not sufficient) condition for two drawings of a graph to be transformable into each other by a sequence of triangle flips is that they have the same ERS. As our main result, we show that for the large class of complete multipartite graphs, this necessary condition is in fact also sufficient. We present two different proofs of this result, one of which is shorter, while the other one yields a polynomial time algorithm for which the number of needed triangle flips for graphs on n vertices is bounded by O(n^{16}). The latter proof uses a Carathéodory-type theorem for simple drawings of complete multipartite graphs, which we believe to be of independent interest.
Moreover, we show that our Gioan-type theorem for complete multipartite graphs is essentially tight in the following sense: For the complete bipartite graph K_{m,n} minus two edges and K_{m,n} plus one edge for any m,n ≥ 4, as well as K_n minus a 4-cycle for any n ≥ 5, there exist two simple drawings with the same ERS that cannot be transformed into each other using triangle flips. So having the same ERS does not remain sufficient when removing or adding very few edges.

Oswin Aichholzer, Man-Kwun Chiu, Hung P. Hoang, Michael Hoffmann, Jan Kynčl, Yannic Maus, Birgit Vogtenhuber, and Alexandra Weinberger. Drawings of Complete Multipartite Graphs up to Triangle Flips. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{aichholzer_et_al:LIPIcs.SoCG.2023.6, author = {Aichholzer, Oswin and Chiu, Man-Kwun and Hoang, Hung P. and Hoffmann, Michael and Kyn\v{c}l, Jan and Maus, Yannic and Vogtenhuber, Birgit and Weinberger, Alexandra}, title = {{Drawings of Complete Multipartite Graphs up to Triangle Flips}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {6:1--6:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-273-0}, ISSN = {1868-8969}, year = {2023}, volume = {258}, editor = {Chambers, Erin W. and Gudmundsson, Joachim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.6}, URN = {urn:nbn:de:0030-drops-178563}, doi = {10.4230/LIPIcs.SoCG.2023.6}, annote = {Keywords: Simple drawings, simple topological graphs, complete graphs, multipartite graphs, k-partite graphs, bipartite graphs, Gioan’s Theorem, triangle flips, Reidemeister moves} }

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

Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal independent set, and coloring problems. A successful line of research has been studying the complexities of LCL problems on paths/cycles, trees, and general graphs, providing many interesting results for the LOCAL model of distributed computing. In this work, we initiate the study of LCL problems in the low-space Massively Parallel Computation (MPC) model. In particular, on forests, we provide a method that, given the complexity of an LCL problem in the LOCAL model, automatically provides an exponentially faster algorithm for the low-space MPC setting that uses optimal global memory, that is, truly linear.
While restricting to forests may seem to weaken the result, we emphasize that all known (conditional) lower bounds for the MPC setting are obtained by lifting lower bounds obtained in the distributed setting in tree-like networks (either forests or high girth graphs), and hence the problems that we study are challenging already on forests. Moreover, the most important technical feature of our algorithms is that they use optimal global memory, that is, memory linear in the number of edges of the graph. In contrast, most of the state-of-the-art algorithms use more than linear global memory. Further, they typically start with a dense graph, sparsify it, and then solve the problem on the residual graph, exploiting the relative increase in global memory. On forests, this is not possible, because the given graph is already as sparse as it can be, and using optimal memory requires new solutions.

Alkida Balliu, Sebastian Brandt, Manuela Fischer, Rustam Latypov, Yannic Maus, Dennis Olivetti, and Jara Uitto. Exponential Speedup over Locality in MPC with Optimal Memory. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2022.9, author = {Balliu, Alkida and Brandt, Sebastian and Fischer, Manuela and Latypov, Rustam and Maus, Yannic and Olivetti, Dennis and Uitto, Jara}, title = {{Exponential Speedup over Locality in MPC with Optimal Memory}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {9:1--9:21}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.9}, URN = {urn:nbn:de:0030-drops-172003}, doi = {10.4230/LIPIcs.DISC.2022.9}, annote = {Keywords: Distributed computing, Locally checkable labeling problems, Trees, Massively Parallel Computation, Sublinear memory} }

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

We present poly log log n-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into k parts such that a node of degree d(u) has ≈ d(u)/k neighbors in each part. Our techniques can be seen as the first progress towards general poly log log n-round algorithms for the Lovász Local Lemma.
As the main application of our result, we obtain a randomized poly log log n-round CONGEST algorithm for (1+ε)Δ-edge coloring n-node graphs of sufficiently large constant maximum degree Δ, for any ε > 0. Further, our results improve the computation of defective colorings and certain tight list coloring problems. All the results improve the state-of-the-art round complexity exponentially, even in the LOCAL model.

Magnús M. Halldórsson, Yannic Maus, and Alexandre Nolin. Fast Distributed Vertex Splitting with Applications. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2022.26, author = {Halld\'{o}rsson, Magn\'{u}s M. and Maus, Yannic and Nolin, Alexandre}, title = {{Fast Distributed Vertex Splitting with Applications}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {26:1--26:24}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.26}, URN = {urn:nbn:de:0030-drops-172176}, doi = {10.4230/LIPIcs.DISC.2022.26}, annote = {Keywords: Graph problems, Edge coloring, List coloring, Lov\'{a}sz local lemma, LOCAL model, CONGEST model, Distributed computing} }

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**Published in:** LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a reconfiguration schedule exists, and the complexity of finding one. A prime example is the reconfiguration of vertex covers. We initiate the study of batched vertex cover reconfiguration, which allows to reconfigure multiple vertices concurrently while requiring that any adversarial reconfiguration order within a batch maintains feasibility. The latter provides robustness, e.g., if the simultaneous reconfiguration of a batch cannot be guaranteed. The quality of a schedule is measured by the number of batches until all nodes are reconfigured, and its cost, i.e., the maximum size of an intermediate vertex cover.
To set a baseline for batch reconfiguration, we show that for graphs belonging to one of the classes {{cycles, trees, forests, chordal, cactus, even-hole-free, claw-free}}, there are schedules that use O(ε^{-1}) batches and incur only a 1+ε multiplicative increase in cost over the best sequential schedules. Our main contribution is to compute such batch schedules in a distributed setting O(ε^{-1} {log^*} n) rounds, which we also show to be tight. Further, we show that once we step out of these graph classes we face a very different situation. There are graph classes on which no efficient distributed algorithm can obtain the best (or almost best) existing schedule. Moreover, there are classes of bounded degree graphs which do not admit any reconfiguration schedules without incurring a large multiplicative increase in the cost at all.

Keren Censor-Hillel, Yannic Maus, Shahar Romem-Peled, and Tigran Tonoyan. Distributed Vertex Cover Reconfiguration. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{censorhillel_et_al:LIPIcs.ITCS.2022.36, author = {Censor-Hillel, Keren and Maus, Yannic and Romem-Peled, Shahar and Tonoyan, Tigran}, title = {{Distributed Vertex Cover Reconfiguration}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {36:1--36:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-217-4}, ISSN = {1868-8969}, year = {2022}, volume = {215}, editor = {Braverman, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.36}, URN = {urn:nbn:de:0030-drops-156327}, doi = {10.4230/LIPIcs.ITCS.2022.36}, annote = {Keywords: reconfiguration, vertex cover, network decomposition} }

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**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-dev.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} }

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

We present a poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complexity between Ω(log n) and poly log log n. Furthermore, we provide extensions to the network decomposition algorithms given in the recent breakthrough by Rozhoň and Ghaffari [STOC2020] and the follow up by Ghaffari, Grunau, and Rozhoň [SODA2021]. In particular, we show how to obtain a large distance separated weak network decomposition with a negligible dependency on the range of unique identifiers.

Yannic Maus and Jara Uitto. Efficient CONGEST Algorithms for the Lovász Local Lemma. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{maus_et_al:LIPIcs.DISC.2021.31, author = {Maus, Yannic and Uitto, Jara}, title = {{Efficient CONGEST Algorithms for the Lov\'{a}sz Local Lemma}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {31:1--31:19}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.31}, URN = {urn:nbn:de:0030-drops-148333}, doi = {10.4230/LIPIcs.DISC.2021.31}, annote = {Keywords: distributed graph algorithms, CONGEST, Lov\'{a}sz Local Lemma, locally checkable labelings} }

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

Linial’s famous color reduction algorithm reduces a given m-coloring of a graph with maximum degree Δ to a O(Δ²log m)-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to choose their color from a list of allowed colors: given an m-coloring in a directed graph of maximum outdegree β, if every node has a list of size Ω(β² (log β+log log m + log log |𝒞|)) from a color space 𝒞 then they can select a color in two rounds in the LOCAL model. Moreover, the communication of a node essentially consists of sending its list to the neighbors. This is obtained as part of a framework that also contains Linial’s color reduction (with an alternative proof) as a special case. Our result also leads to a defective list coloring algorithm. As a corollary, we improve the state-of-the-art truly local (deg+1)-list coloring algorithm from Barenboim et al. [PODC'18] by slightly reducing the runtime to O(√{ΔlogΔ})+log^* n and significantly reducing the message size (from huge to roughly Δ). Our techniques are inspired by the local conflict coloring framework of Fraigniaud et al. [FOCS'16].

Yannic Maus and Tigran Tonoyan. Local Conflict Coloring Revisited: Linial for Lists. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{maus_et_al:LIPIcs.DISC.2020.16, author = {Maus, Yannic and Tonoyan, Tigran}, title = {{Local Conflict Coloring Revisited: Linial for Lists}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {16:1--16:18}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.16}, URN = {urn:nbn:de:0030-drops-130944}, doi = {10.4230/LIPIcs.DISC.2020.16}, annote = {Keywords: distributed graph coloring, list coloring, low intersecting set families} }

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

We give an improved randomized CONGEST algorithm for distance-2 coloring that uses Δ²+1 colors and runs in O(log n) rounds, improving the recent O(log Δ ⋅ log n)-round algorithm in [Halldórsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to O(log Δ) + 2^{O(√{log log n})}.

Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin. Coloring Fast Without Learning Your Neighbors' Colors. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2020.39, author = {Halld\'{o}rsson, Magn\'{u}s M. and Kuhn, Fabian and Maus, Yannic and Nolin, Alexandre}, title = {{Coloring Fast Without Learning Your Neighbors' Colors}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {39:1--39:17}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.39}, URN = {urn:nbn:de:0030-drops-131170}, doi = {10.4230/LIPIcs.DISC.2020.39}, annote = {Keywords: distributed graph coloring, distance 2 coloring, congestion} }

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Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

We study a process of averaging in a distributed system with noisy communication. Each of the agents in the system starts with some value and the goal of each agent is to compute the average of all the initial values. In each round, one pair of agents is drawn uniformly at random from the whole population, communicates with each other and each of these two agents updates their local value based on their own value and the received message. The communication is noisy and whenever an agent sends any value v, the receiving agent receives v+N, where N is a zero-mean Gaussian random variable. The two quality measures of interest are (i) the total sum of squares TSS(t), which measures the sum of square distances from the average load to the initial average and (ii) bar{phi}(t), which measures the sum of square distances from the average load to the running average (average at time t).
It is known that the simple averaging protocol - in which an agent sends its current value and sets its new value to the average of the received value and its current value - converges eventually to a state where bar{phi}(t) is small. It has been observed that TSS(t), due to the noise, eventually diverges and previous research - mostly in control theory - has focused on showing eventual convergence w.r.t. the running average. We obtain the first probabilistic bounds on the convergence time of bar{phi}(t) and precise bounds on the drift of TSS(t) that show that although TSS(t) eventually diverges, for a wide and interesting range of parameters, TSS(t) stays small for a number of rounds that is polynomial in the number of agents. Our results extend to the synchronous setting and settings where the agents are restricted to discrete values and perform rounding.

Frederik Mallmann-Trenn, Yannic Maus, and Dominik Pajak. Noidy Conmunixatipn: On the Convergence of the Averaging Population Protocol. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 148:1-148:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mallmanntrenn_et_al:LIPIcs.ICALP.2019.148, author = {Mallmann-Trenn, Frederik and Maus, Yannic and Pajak, Dominik}, title = {{Noidy Conmunixatipn: On the Convergence of the Averaging Population Protocol}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {148:1--148:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.148}, URN = {urn:nbn:de:0030-drops-107240}, doi = {10.4230/LIPIcs.ICALP.2019.148}, annote = {Keywords: population protocols, noisy communication, distributed averaging} }

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Brief Announcement

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

We define a generalization of local distributed graph problems to (synchronous round-based) dynamic networks and present a framework for developing algorithms for these problems. We require two properties from our algorithms: (1) They should satisfy non-trivial guarantees in every round. The guarantees should be stronger the more stable the graph has been during the last few rounds and they coincide with the definition of the static graph problem if no topological change appeared recently. (2) If a constant neighborhood around some part of the graph is stable during an interval, the algorithms quickly converge to a solution for this part of the graph that remains unchanged throughout the interval.
We demonstrate our generic framework with two classic distributed graph, namely (degree+1)-vertex coloring and maximal independent set (MIS).

Philipp Bamberger, Fabian Kuhn, and Yannic Maus. Brief Announcement: Local Distributed Algorithms in Highly Dynamic Networks. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 42:1-42:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bamberger_et_al:LIPIcs.DISC.2018.42, author = {Bamberger, Philipp and Kuhn, Fabian and Maus, Yannic}, title = {{Brief Announcement: Local Distributed Algorithms in Highly Dynamic Networks}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {42:1--42:4}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.42}, URN = {urn:nbn:de:0030-drops-98318}, doi = {10.4230/LIPIcs.DISC.2018.42}, annote = {Keywords: dynamic networks, distributed graph algorithms, MIS, vertex coloring} }

Document

**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-dev.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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