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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)

Counting the number of nodes in {Anonymous Dynamic Networks} is enticing from an algorithmic perspective: an important computation in a restricted platform with promising applications. Starting with Michail, Chatzigiannakis, and Spirakis [Michail et al., 2013], a flurry of papers sped up the running time guarantees from doubly-exponential to polynomial [Dariusz R. Kowalski and Miguel A. Mosteiro, 2018]. There is a common theme across all those works: a distinguished node is assumed to be present, because Counting cannot be solved deterministically without at least one.
In the present work we study challenging questions that naturally follow: how to efficiently count with more than one distinguished node, or how to count without any distinguished node. More importantly, what is the minimal information needed about these distinguished nodes and what is the best we can aim for (count precision, stochastic guarantees, etc.) without any. We present negative and positive results to answer these questions. To the best of our knowledge, this is the first work that addresses them.

Dariusz R. Kowalski and Miguel A. Mosteiro. Polynomial Anonymous Dynamic Distributed Computing Without a Unique Leader. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 147:1-147:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kowalski_et_al:LIPIcs.ICALP.2019.147, author = {Kowalski, Dariusz R. and Mosteiro, Miguel A.}, title = {{Polynomial Anonymous Dynamic Distributed Computing Without a Unique Leader}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {147:1--147:15}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.147}, URN = {urn:nbn:de:0030-drops-107239}, doi = {10.4230/LIPIcs.ICALP.2019.147}, annote = {Keywords: Anonymous Dynamic Networks, Counting, distributed algorithms} }

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**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Starting with Michail, Chatzigiannakis, and Spirakis work [Michail et al., 2013], the problem of Counting the number of nodes in {Anonymous Dynamic Networks} has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program) and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing as the number of participants is frequently needed to make important decisions, such as termination, agreement, synchronization, and many others. A variety of algorithms built on top of mass-distribution techniques have been presented, analyzed, and also experimentally evaluated; some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees.

Dariusz R. Kowalski and Miguel A. Mosteiro. Polynomial Counting in Anonymous Dynamic Networks with Applications to Anonymous Dynamic Algebraic Computations. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 156:1-156:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kowalski_et_al:LIPIcs.ICALP.2018.156, author = {Kowalski, Dariusz R. and Mosteiro, Miguel A.}, title = {{Polynomial Counting in Anonymous Dynamic Networks with Applications to Anonymous Dynamic Algebraic Computations}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {156:1--156:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.156}, URN = {urn:nbn:de:0030-drops-91602}, doi = {10.4230/LIPIcs.ICALP.2018.156}, annote = {Keywords: Anonymous Dynamic Networks, Counting, Boolean functions, distributed algorithms, deterministic algorithms} }

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**Published in:** LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)

Information dissemination protocols for ad-hoc wireless networks frequently use a minimal subset of the available communication links, defining a rooted "“broadcast"” tree. In this work, we focus on the core challenge of disseminating from one layer to the next one of such tree. We call this problem Layer Dissemination. We study Layer Dissemination under a generalized model of interference, called affectance. The affectance model subsumes previous models, such as Radio Network and Signal to Inteference-plus-Noise Ratio. We present randomized and deterministic protocols for Layer Dissemination. These protocols are based on a combinatorial object that we call Affectance-selective Families. Our approach combines an engineering solution with theoretical guarantees. That is, we provide a method to characterize the network with a global measure of affectance based on measurements of interference in the specific deployment area. Then, our protocols distributedly produce an ad-hoc transmissions schedule for dissemination. In the randomized protocol only the network characterization is needed, whereas the deterministic protocol requires full knowledge of affectance. Our theoretical analysis provides guarantees on schedule length. We also present simulations of a real network-deployment area contrasting the perform- ance of our randomized protocol, which takes into account affectance, against previous work for interference models that ignore some physical constraints. The striking improvement in performance shown by our simulations show the importance of utilizing a more physically-accurate model of interference that takes into account other effects beyond distance to transmitters.

Harshita Kudaravalli and Miguel A. Mosteiro. Ad-Hoc Affectance-Selective Families for Layer Dissemination. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kudaravalli_et_al:LIPIcs.SEA.2017.33, author = {Kudaravalli, Harshita and Mosteiro, Miguel A.}, title = {{Ad-Hoc Affectance-Selective Families for Layer Dissemination}}, booktitle = {16th International Symposium on Experimental Algorithms (SEA 2017)}, pages = {33:1--33:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-036-1}, ISSN = {1868-8969}, year = {2017}, volume = {75}, editor = {Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.33}, URN = {urn:nbn:de:0030-drops-76064}, doi = {10.4230/LIPIcs.SEA.2017.33}, annote = {Keywords: Wireless Networks, Broadcast Protocols, Affectance, SINR} }

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

We study the problem of counting the number of nodes in a slotted-time communication network, under the challenging assumption that nodes do not have identifiers and the network topology changes frequently. That is, for each time slot links among nodes can change arbitrarily provided that the network is always connected.
This network model has been motivated by the ongoing development of new communication technologies that enable the deployment of a massive number of devices with highly dynamic connectivity patterns. Tolerating dynamic topologies is clearly crucial in face of mobility and unreliable communication. Current communication networks do have node identifiers though. Nevertheless, in future massive networks, it might be suitable to avoid nodes IDs to facilitate mass production. Consequently, knowing what is the cost of anonymity is of paramount importance to understand what is feasible or not for future generations of Dynamic Networks.
Counting is a fundamental task in distributed computing since knowing the size of the system often facilitates the desing of solutions for more complex problems. Also, the size of the system is usually used to decide termination in distributed algorithms. Currently, the best upper bound proved on the running time to compute the exact network size is double-exponential. However, only linear complexity lower bounds are known, leaving open the question of whether efficient Counting protocols for Anonymous Dynamic Networks exist or not.
In this paper we make a significant step towards answering this question by presenting a distributed Counting protocol for Anonymous Dynamic Networks which has exponential time complexity. This algorithm, which we call Incremental Counting, ensures that eventually every node knows the exact size of the system and stops executing the protocol. Previous Counting protocols have either double-exponential time complexity, or they are exponential but do not terminate, or terminate but do not provide running-time guarantees, or guarantee only an exponential upper bound on the network size. Other protocols are heuristic and do not guarantee the correct count.

Alessia Milani and Miguel A. Mosteiro. A Faster Counting Protocol for Anonymous Dynamic Networks. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{milani_et_al:LIPIcs.OPODIS.2015.28, author = {Milani, Alessia and Mosteiro, Miguel A.}, title = {{A Faster Counting Protocol for Anonymous Dynamic Networks}}, booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)}, pages = {28:1--28:13}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.28}, URN = {urn:nbn:de:0030-drops-66179}, doi = {10.4230/LIPIcs.OPODIS.2015.28}, annote = {Keywords: Anonymous Dynamic Networks, Counting, Time-varying Graphs} }