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Invited Talk

**Published in:** LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Recent advances in the design of efficient parallel algorithms have been largely focusing on the nowadays classical model of parallel computing called Massive Parallel Computation (MPC), which follows the framework of MapReduce systems. In this talk we will survey recent advances in the design of algorithms for graph problems for the MPC model and will mention some interesting open questions in this area.

Artur Czumaj. Modern Parallel Algorithms (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{czumaj:LIPIcs.MFCS.2023.3, author = {Czumaj, Artur}, title = {{Modern Parallel Algorithms}}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}, pages = {3:1--3:2}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-292-1}, ISSN = {1868-8969}, year = {2023}, volume = {272}, editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.3}, URN = {urn:nbn:de:0030-drops-185378}, doi = {10.4230/LIPIcs.MFCS.2023.3}, annote = {Keywords: Distributed computing, parallel computing} }

Document

Track A: Algorithms, Complexity and Games

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

We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node u of degree d(u) is assigned a palette of d(u)+1 colors, and the goal is to find a proper coloring using these color palettes. The (degree+1)-list coloring problem is a natural generalization of the classical (Δ+1)-coloring and (Δ+1)-list coloring problems, both being benchmark problems extensively studied in distributed and parallel computing.
In this paper we settle the complexity of the (degree+1)-list coloring problem in the Congested Clique model by showing that it can be solved deterministically in a constant number of rounds.

Sam Coy, Artur Czumaj, Peter Davies, and Gopinath Mishra. Optimal (Degree+1)-Coloring in Congested Clique. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{coy_et_al:LIPIcs.ICALP.2023.46, author = {Coy, Sam and Czumaj, Artur and Davies, Peter and Mishra, Gopinath}, title = {{Optimal (Degree+1)-Coloring in Congested Clique}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {46:1--46:20}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.46}, URN = {urn:nbn:de:0030-drops-180987}, doi = {10.4230/LIPIcs.ICALP.2023.46}, annote = {Keywords: Distributed computing, graph coloring, parallel computing} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

We consider an important generalization of the Steiner tree problem, the Steiner forest problem, in the Euclidean plane: the input is a multiset X ⊆ ℝ², partitioned into k color classes C₁, C₂, …, Cₖ ⊆ X. The goal is to find a minimum-cost Euclidean graph G such that every color class Cᵢ is connected in G. We study this Steiner forest problem in the streaming setting, where the stream consists of insertions and deletions of points to X. Each input point x ∈ X arrives with its color color(x) ∈ [k], and as usual for dynamic geometric streams, the input is restricted to the discrete grid {0, …, Δ}².
We design a single-pass streaming algorithm that uses poly(k ⋅ log Δ) space and time, and estimates the cost of an optimal Steiner forest solution within ratio arbitrarily close to the famous Euclidean Steiner ratio α₂ (currently 1.1547 ≤ α₂ ≤ 1.214). This approximation guarantee matches the state of the art bound for streaming Steiner tree, i.e., when k = 1. Our approach relies on a novel combination of streaming techniques, like sampling and linear sketching, with the classical Arora-style dynamic-programming framework for geometric optimization problems, which usually requires large memory and has so far not been applied in the streaming setting.
We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite approximation requires Ω(k) bits of space.

Artur Czumaj, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý. Streaming Algorithms for Geometric Steiner Forest. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 47:1-47:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2022.47, author = {Czumaj, Artur and Jiang, Shaofeng H.-C. and Krauthgamer, Robert and Vesel\'{y}, Pavel}, title = {{Streaming Algorithms for Geometric Steiner Forest}}, booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)}, pages = {47:1--47:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-235-8}, ISSN = {1868-8969}, year = {2022}, volume = {229}, editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.47}, URN = {urn:nbn:de:0030-drops-163880}, doi = {10.4230/LIPIcs.ICALP.2022.47}, annote = {Keywords: Steiner forest, streaming, sublinear algorithms, dynamic programming} }

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Complete Volume

**Published in:** LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

LIPIcs, Volume 227, SWAT 2022, Complete Volume

18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 1-558, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{czumaj_et_al:LIPIcs.SWAT.2022, title = {{LIPIcs, Volume 227, SWAT 2022, Complete Volume}}, booktitle = {18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)}, pages = {1--558}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-236-5}, ISSN = {1868-8969}, year = {2022}, volume = {227}, editor = {Czumaj, Artur and Xin, Qin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022}, URN = {urn:nbn:de:0030-drops-161599}, doi = {10.4230/LIPIcs.SWAT.2022}, annote = {Keywords: LIPIcs, Volume 227, SWAT 2022, Complete Volume} }

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Front Matter

**Published in:** LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Front Matter, Table of Contents, Preface, Conference Organization

18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{czumaj_et_al:LIPIcs.SWAT.2022.0, author = {Czumaj, Artur and Xin, Qin}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)}, pages = {0:i--0:x}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-236-5}, ISSN = {1868-8969}, year = {2022}, volume = {227}, editor = {Czumaj, Artur and Xin, Qin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.0}, URN = {urn:nbn:de:0030-drops-161602}, doi = {10.4230/LIPIcs.SWAT.2022.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

**Published in:** LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Hybrid networks, i.e., networks that leverage different means of communication, become ever more widespread. To allow theoretical study of such networks, [Augustine et al., SODA'20] introduced the HYBRID model, which is based on the concept of synchronous message passing and uses two fundamentally different principles of communication: a local mode, which allows every node to exchange one message per round with each neighbor in a local communication graph; and a global mode where any pair of nodes can exchange messages, but only few such exchanges can take place per round. A sizable portion of the previous research for the HYBRID model revolves around basic communication primitives and computing distances or shortest paths in networks. In this paper, we extend this study to a related fundamental problem of computing compact routing schemes for near-shortest paths in the local communication graph. We demonstrate that, for the case where the local communication graph is a unit-disc graph with n nodes that is realized in the plane and has no radio holes, we can deterministically compute a routing scheme that has constant stretch and uses labels and local routing tables of size O(log n) bits in only O(log n) rounds.

Sam Coy, Artur Czumaj, Michael Feldmann, Kristian Hinnenthal, Fabian Kuhn, Christian Scheideler, Philipp Schneider, and Martijn Struijs. Near-Shortest Path Routing in Hybrid Communication Networks. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{coy_et_al:LIPIcs.OPODIS.2021.11, author = {Coy, Sam and Czumaj, Artur and Feldmann, Michael and Hinnenthal, Kristian and Kuhn, Fabian and Scheideler, Christian and Schneider, Philipp and Struijs, Martijn}, title = {{Near-Shortest Path Routing in Hybrid Communication Networks}}, booktitle = {25th International Conference on Principles of Distributed Systems (OPODIS 2021)}, pages = {11:1--11:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-219-8}, ISSN = {1868-8969}, year = {2022}, volume = {217}, editor = {Bramas, Quentin and Gramoli, Vincent and Milani, Alessia}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.11}, URN = {urn:nbn:de:0030-drops-157863}, doi = {10.4230/LIPIcs.OPODIS.2021.11}, annote = {Keywords: Hybrid networks, overlay networks} }

Document

Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

We want to efficiently find a specific object in a large unstructured set, which we model by a random n-permutation, and we have to do it by revealing just a single element. Clearly, without any help this task is hopeless and the best one can do is to select the element at random, and achieve the success probability 1/n. Can we do better with some small amount of advice about the permutation, even without knowing the object sought? We show that by providing advice of just one integer in {0,1,… ,n-1}, one can improve the success probability considerably, by a Θ((log n)/(log log n)) factor.
We study this and related problems, and show asymptotically matching upper and lower bounds for their optimal probability of success. Our analysis relies on a close relationship of such problems to some intrinsic properties of random permutations related to the rencontres number.

Artur Czumaj, George Kontogeorgiou, and Mike Paterson. Haystack Hunting Hints and Locker Room Communication. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2021.58, author = {Czumaj, Artur and Kontogeorgiou, George and Paterson, Mike}, title = {{Haystack Hunting Hints and Locker Room Communication}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {58:1--58:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-195-5}, ISSN = {1868-8969}, year = {2021}, volume = {198}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.58}, URN = {urn:nbn:de:0030-drops-141270}, doi = {10.4230/LIPIcs.ICALP.2021.58}, annote = {Keywords: Random permutations, Search, Communication complexity} }

Document

RANDOM

**Published in:** LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

We consider the fundamental question of understanding the relative power of two important computational models: property testing and data streaming. We present a novel framework closely linking these areas in the setting of general graphs in the context of constant-query complexity testing and constant-space streaming. Our main result is a generic transformation of a one-sided error property tester in the random-neighbor model with constant query complexity into a one-sided error property tester in the streaming model with constant space complexity. Previously such a generic transformation was only known for bounded-degree graphs.

Artur Czumaj, Hendrik Fichtenberger, Pan Peng, and Christian Sohler. Testable Properties in General Graphs and Random Order Streaming. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{czumaj_et_al:LIPIcs.APPROX/RANDOM.2020.16, author = {Czumaj, Artur and Fichtenberger, Hendrik and Peng, Pan and Sohler, Christian}, title = {{Testable Properties in General Graphs and Random Order Streaming}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, pages = {16:1--16:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-164-1}, ISSN = {1868-8969}, year = {2020}, volume = {176}, editor = {Byrka, Jaros{\l}aw and Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.16}, URN = {urn:nbn:de:0030-drops-126190}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.16}, annote = {Keywords: Graph property testing, sublinear algorithms, graph streaming algorithms} }

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Complete Volume

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

LIPIcs, Volume 168, ICALP 2020, Complete Volume

47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 1-2446, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{czumaj_et_al:LIPIcs.ICALP.2020, title = {{LIPIcs, Volume 168, ICALP 2020, Complete Volume}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {1--2446}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020}, URN = {urn:nbn:de:0030-drops-124067}, doi = {10.4230/LIPIcs.ICALP.2020}, annote = {Keywords: LIPIcs, Volume 168, ICALP 2020, Complete Volume} }

Document

Front Matter

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Front Matter, Table of Contents, Preface, Conference Organization

47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 0:i-0:xxxvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2020.0, author = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {0:i--0:xxxvi}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.0}, URN = {urn:nbn:de:0030-drops-124075}, doi = {10.4230/LIPIcs.ICALP.2020.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

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

Ad-hoc radio networks and multiple access channels are classical and well-studied models of distributed systems, with a large body of literature on deterministic algorithms for fundamental communications primitives such as broadcasting and wake-up. However, almost all of these algorithms assume knowledge of the number of participating nodes and the range of possible IDs, and often make the further assumption that the latter is linear in the former. These are very strong assumptions for models which were designed to capture networks of weak devices organized in an ad-hoc manner. It was believed that without this knowledge, deterministic algorithms must necessarily be much less efficient.
In this paper we address this fundamental question and show that this is not the case. We present deterministic algorithms for blind networks (in which nodes know only their own IDs), which match or nearly match the running times of the fastest algorithms which assume network knowledge (and even surpass the previous fastest algorithms which assume parameter knowledge but not small labels).
Specifically, in multiple access channels with k participating nodes and IDs up to L, we give a wake-up algorithm requiring O((k log L log k)/(log log k)) time, improving dramatically over the O(L^3 log^3 L) time algorithm of De Marco et al. (2007), and a broadcasting algorithm requiring O(k log L log log k) time, improving over the O(L) time algorithm of Gasieniec et al. (2001) in most circumstances. Furthermore, we show how these same algorithms apply directly to multi-hop radio networks, achieving even larger running time improvements.

Artur Czumaj and Peter Davies. Deterministic Blind Radio Networks. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{czumaj_et_al:LIPIcs.DISC.2018.15, author = {Czumaj, Artur and Davies, Peter}, title = {{Deterministic Blind Radio Networks}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {15:1--15:17}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.15}, URN = {urn:nbn:de:0030-drops-98047}, doi = {10.4230/LIPIcs.DISC.2018.15}, annote = {Keywords: Broadcasting, Deterministic Algorithms, Radio Networks} }

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

The problem of detecting network structures plays a central role in distributed computing. One of the fundamental problems studied in this area is to determine whether for a given graph H, the input network contains a subgraph isomorphic to H or not. We investigate this problem for H being a clique K_l in the classical distributed CONGEST model, where the communication topology is the same as the topology of the underlying network, and with limited communication bandwidth on the links.
Our first and main result is a lower bound, showing that detecting K_l requires Omega(sqrt{n} / b) communication rounds, for every 4 <=l <=sqrt{n}, and Omega(n / (l b)) rounds for every l >= sqrt{n}, where b is the bandwidth of the communication links. This result is obtained by using a reduction to the set disjointness problem in the framework of two-party communication complexity. We complement our lower bound with a two-party communication protocol for listing all cliques in the input graph, which up to constant factors communicates the same number of bits as our lower bound for K_4 detection. This demonstrates that our lower bound cannot be improved using the two-party communication framework.

Artur Czumaj and Christian Konrad. Detecting Cliques in CONGEST Networks. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{czumaj_et_al:LIPIcs.DISC.2018.16, author = {Czumaj, Artur and Konrad, Christian}, title = {{Detecting Cliques in CONGEST Networks}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {16:1--16:15}, 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.2018.16}, URN = {urn:nbn:de:0030-drops-98057}, doi = {10.4230/LIPIcs.DISC.2018.16}, annote = {Keywords: Lower bounds, CONGEST, subgraph detection, two-party communication} }

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Brief Announcement

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

Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. Much work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental communications tasks such as broadcasting. Most of these algorithms, however, assume that devices have some network knowledge (usually bounds on the number of nodes in the network n, and the diameter D), which may not be realistic in systems with weak devices or gradual deployment. Little is known about what can be done without this information.
This is the issue we address in this work, by presenting the first randomized broadcasting algorithms for blind networks in which nodes have no prior knowledge whatsoever. We demonstrate that lack of parameter knowledge can be overcome at only a small increase in running time. Specifically, we show that in networks without collision detection, broadcast can be achieved in O(D log n/D log^2 log n/D + log^2 n) time, almost reaching the Omega(D log n/D + log^2 n) lower bound. We also give an even faster algorithm for directed networks with collision detection.

Artur Czumaj and Peter Davies. Brief Announcement: Randomized Blind Radio Networks. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{czumaj_et_al:LIPIcs.DISC.2018.43, author = {Czumaj, Artur and Davies, Peter}, title = {{Brief Announcement: Randomized Blind Radio Networks}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {43:1--43:3}, 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.2018.43}, URN = {urn:nbn:de:0030-drops-98323}, doi = {10.4230/LIPIcs.DISC.2018.43}, annote = {Keywords: Broadcasting, Randomized Algorithms, Radio Networks} }

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**Published in:** LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

In this paper we study three previously unstudied variants of the online Facility Location problem, considering an intrinsic scenario when the clients and facilities are not only allowed to arrive to the system, but they can also depart at any moment.
We begin with the study of a natural fully-dynamic online uncapacitated model where clients can be both added and removed. When a client arrives, then it has to be assigned either to an existing facility or to a new facility opened at the client's location. However, when a client who has been also one of the open facilities is to be removed, then our model has to allow to reconnect all clients that have been connected to that removed facility. In this model, we present an optimal O(log(n_{act}) / log log(n_{act}))-competitive algorithm, where n_{act} is the number of active clients at the end of the input sequence.
Next, we turn our attention to the capacitated Facility Location problem. We first note that if no deletions are allowed, then one can achieve an optimal competitive ratio of O(log(n) / log(log n)), where n is the length of the sequence. However, when deletions are allowed, the capacitated version of the problem is significantly more challenging than the uncapacitated one. We show that still, using a more sophisticated algorithmic approach, one can obtain an online O(log N + log c log n)-competitive algorithm for the capacitated Facility Location problem in the fully dynamic model, where N is number of points in the input metric and c is the capacity of any open facility.

Marek Cygan, Artur Czumaj, Marcin Mucha, and Piotr Sankowski. Online Facility Location with Deletions. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cygan_et_al:LIPIcs.ESA.2018.21, author = {Cygan, Marek and Czumaj, Artur and Mucha, Marcin and Sankowski, Piotr}, title = {{Online Facility Location with Deletions}}, booktitle = {26th Annual European Symposium on Algorithms (ESA 2018)}, pages = {21:1--21:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-081-1}, ISSN = {1868-8969}, year = {2018}, volume = {112}, editor = {Azar, Yossi and Bast, Hannah and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.21}, URN = {urn:nbn:de:0030-drops-94843}, doi = {10.4230/LIPIcs.ESA.2018.21}, annote = {Keywords: online algorithms, facility location, fully-dynamic online algorithms} }

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**Published in:** LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

The beep model is a very weak communications model in which devices in a network can communicate only via beeps and silence. As a result of its weak assumptions, it has broad applicability to many different implementations of communications networks. This comes at the cost of a restrictive environment for algorithm design.
Despite being only recently introduced, the beep model has received considerable attention, in part due to its relationship with other communication models such as that of ad-hoc radio networks. However, there has been no definitive published result for several fundamental tasks in the model. We aim to rectify this with our paper.
We present algorithms for the tasks of broadcast, gossiping, and multi-broadcast, and also, as intermediary results, means of depth-first search and diameter estimation. Our O(D+log(M)-time algorithm for broadcasting is a simple formalization of a concept known as beep waves, and is asymptotically optimal. We give an O(n*log(L))-time depth-first search procedure, and show how this can be used as the basis for an O(n*log(L*M))-time gossiping algorithm. Finally, we approach the more general problem of multi-broadcast. We differentiate between two variants of this problem: one where nodes must know the origin of all source messages, and another where this information is not required. In the first instance we achieve an algorithm running in time O(k*log((L*M)/k)+D*log(L)), and in the second an O(k*log(M/k)+D*log(L))-time algorithm (or O(M+D*log(L)) when M <= k). We then give corresponding lower bounds: Omega(k*log((L*M)/k)+D) in the case where nodes must know message origins, and Omega(k*log(M/k)+D) and Omega(M+D) in the other case, for M > k and M <= k respectively. These lower bounds demonstrate that our algorithms are optimal except for the D*log(L) additive term. In these running-time expressions, n represents network size, D network diameter, L range of node labels, M range of source messages, and k number of sources.
Our algorithms are all explicit, deterministic, and practical, and give efficient means of communication while making arguably the minimum possible assumptions about the network.

Artur Czumaj and Peter Davies. Communicating with Beeps. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{czumaj_et_al:LIPIcs.OPODIS.2015.30, author = {Czumaj, Artur and Davies, Peter}, title = {{Communicating with Beeps}}, booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)}, pages = {30:1--30:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-98-9}, ISSN = {1868-8969}, year = {2016}, volume = {46}, editor = {Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.30}, URN = {urn:nbn:de:0030-drops-66195}, doi = {10.4230/LIPIcs.OPODIS.2015.30}, annote = {Keywords: Beep model, Communication networks, Broadcasting, Gossiping, Leader election} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

In this paper we improve the deterministic complexity of two fundamental communication primitives in the classical model of ad-hoc radio networks with unknown topology: broadcasting and wake-up. We consider an unknown radio network, in which all nodes have no prior knowledge about network topology, and know only the size of the network n, the maximum in-degree of any node Delta, and the eccentricity of the network D.
For such networks, we first give an algorithm for wake-up, in both directed and undirected networks, based on the existence of small universal synchronizers. This algorithm runs in O((min{n,D*Delta}*log(n)*log(Delta))/(log(log(Delta)))) time, improving over the previous best O(n*log^2(n))-time result across all ranges of parameters, but particularly when maximum in-degree is small.
Next, we introduce a new combinatorial framework of block synchronizers and prove the existence of such objects of low size. Using this framework, we design a new deterministic algorithm for the fundamental problem of broadcasting, running in O(n*log(D)*log(log((D*Delta)/n))) time. This is the fastest known algorithm for this problems, improving upon the O(n*log(n)*log*log(n))-time algorithm of De Marco (2010) and the O(n*log^2(D))-time algorithm due to Czumaj and Rytter (2003), the previous fastest results for directed networks, and is the first to come within a log-logarithmic factor of the Omega(n*log(D)) lower bound due to Clementi et al. (2003).
Our results have also direct implications on the fastest deterministic leader election and clock synchronization algorithms in both directed and undirected radio networks, tasks which are commonly used as building blocks for more complex procedures.

Artur Czumaj and Peter Davies. Faster Deterministic Communication in Radio Networks. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 139:1-139:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2016.139, author = {Czumaj, Artur and Davies, Peter}, title = {{Faster Deterministic Communication in Radio Networks}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {139:1--139:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.139}, URN = {urn:nbn:de:0030-drops-62838}, doi = {10.4230/LIPIcs.ICALP.2016.139}, annote = {Keywords: Radio networks, Communication networks, Broadcasting, Wake-Up, Deterministic algorithms} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 8341, Sublinear Algorithms (2008)

From August 17 to August 22, 2008, the Dagstuhl Seminar 08341 ``Sublinear Algorithms'' was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 08341 Abstracts Collection – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{czumaj_et_al:DagSemProc.08341.1, author = {Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian}, title = {{08341 Abstracts Collection – Sublinear Algorithms}}, booktitle = {Sublinear Algorithms}, pages = {1--19}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8341}, 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.08341.1}, URN = {urn:nbn:de:0030-drops-16981}, doi = {10.4230/DagSemProc.08341.1}, annote = {Keywords: Sublinear algorithms, property testing, data streaming, graph algorithms, approximation algorithms} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 8341, Sublinear Algorithms (2008)

This report summarizes the content and structure of the Dagstuhl seminar `Sublinear Algorithms', which was held from 17.8.2008 to 22.8.2008 in Schloss Dagstuhl, Germany.

Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 08341 Executive Summary – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{czumaj_et_al:DagSemProc.08341.2, author = {Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian}, title = {{08341 Executive Summary – Sublinear Algorithms}}, booktitle = {Sublinear Algorithms}, pages = {1--2}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8341}, 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.08341.2}, URN = {urn:nbn:de:0030-drops-16964}, doi = {10.4230/DagSemProc.08341.2}, annote = {Keywords: Sublinear algorithms, property testing, data streaming, graph algorithms, approximation algorithms} }

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

From 17.07.05 to 22.07.05, the Dagstuhl Seminar
05291 ``Sublinear Algorithms'' was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 05291 Abstracts Collection – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 5291, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{czumaj_et_al:DagSemProc.05291.1, author = {Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian}, title = {{05291 Abstracts Collection – Sublinear 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.05291.1}, URN = {urn:nbn:de:0030-drops-6814}, doi = {10.4230/DagSemProc.05291.1}, annote = {Keywords: Property testing, sublinear time approximation algorithms, data streaming algorithms} }

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