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**Published in:** LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

In this paper, we settle the main open question of [Michail, Skretas, Spirakis, ICALP'17], asking what is the family of two-dimensional geometric shapes that can be transformed into each other by a sequence of rotation operations, none of which disconnects the shape. The model represents programmable matter systems consisting of interconnected modules that perform the minimal mechanical operation of 90° rotations around each other. The goal is to transform an initial shape of modules A into a target shape B. Under the necessary assumptions that the given shapes are connected and have identical colourings on a checkered colouring of the grid, and using a seed of only constant size, we prove that any pair of such shapes can be transformed into each other within an optimal O(n²) rotation operations none of which disconnects the shape.

Matthew Connor, Othon Michail, and George Skretas. All for One and One for All: An O(1)-Musketeers Universal Transformation for Rotating Robots. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{connor_et_al:LIPIcs.SAND.2024.9, author = {Connor, Matthew and Michail, Othon and Skretas, George}, title = {{All for One and One for All: An O(1)-Musketeers Universal Transformation for Rotating Robots}}, booktitle = {3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)}, pages = {9:1--9:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-315-7}, ISSN = {1868-8969}, year = {2024}, volume = {292}, editor = {Casteigts, Arnaud and Kuhn, Fabian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.9}, URN = {urn:nbn:de:0030-drops-198874}, doi = {10.4230/LIPIcs.SAND.2024.9}, annote = {Keywords: programmable matter, universal transformation, reconfigurable robotics, shape formation, centralised algorithms} }

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Brief Announcement

**Published in:** LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

We explore how geometric structures (or shapes) can be grown exponentially fast from a single node, through a sequence of centralized growth operations, and if collisions during growth are to be avoided. We identify a parameter k, representing the number of turning points within specific parts of a shape. We prove that, if edges can only be formed when generating new nodes and cannot be deleted, trees having O(k) turning points on every root-to-leaf path can be grown in O(klog n) time steps and spirals with O(log n) turning points can be grown in O(log n) time steps, n being the size of the final shape. For this case, we also show that the maximum number of turning points in a root-to-leaf path of a tree is a lower bound on the number of time steps to grow the tree and that there exists a class of paths such that any path in the class with Ω(k) turning points requires Ω(klog k) time steps to be grown. In the stronger model, where edges can be deleted and neighbors can be handed over to newly generated nodes, we obtain a universal algorithm: for any shape S it gives a process that grows S from a single node exponentially fast.

Nada Almalki, Siddharth Gupta, and Othon Michail. Brief Announcement: On the Exponential Growth of Geometric Shapes. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 23:1-23:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{almalki_et_al:LIPIcs.SAND.2024.23, author = {Almalki, Nada and Gupta, Siddharth and Michail, Othon}, title = {{Brief Announcement: On the Exponential Growth of Geometric Shapes}}, booktitle = {3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)}, pages = {23:1--23:6}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-315-7}, ISSN = {1868-8969}, year = {2024}, volume = {292}, editor = {Casteigts, Arnaud and Kuhn, Fabian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.23}, URN = {urn:nbn:de:0030-drops-199015}, doi = {10.4230/LIPIcs.SAND.2024.23}, annote = {Keywords: centralized algorithm, growth process, collision, programmable matter} }

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Brief Announcement

**Published in:** LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

We consider geometric collision-detection problems for modular reconfigurable robots. Assuming the nodes (modules) are connected squares on a grid, we investigate the complexity of deciding whether collisions may occur, or can be avoided, if a set of expansion and contraction operations is executed. We study both discrete- and continuous-time models, and allow operations to be coupled into a single parallel group. Our algorithms to decide if a collision may occur run in O(n²log² n) time, O(n²) time, or O(nlog² n) time, depending on the presence and type of coupled operations, in a continuous-time model for a modular robot with n nodes. To decide if collisions can be avoided, we show that a very restricted version is already NP-complete in the discrete-time model, while the same problem is polynomial in the continuous-time model. A less restricted version is NP-hard in the continuous-time model.

Siddharth Gupta, Marc van Kreveld, Othon Michail, and Andreas Padalkin. Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 26:1-26:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gupta_et_al:LIPIcs.SAND.2024.26, author = {Gupta, Siddharth and van Kreveld, Marc and Michail, Othon and Padalkin, Andreas}, title = {{Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them}}, booktitle = {3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)}, pages = {26:1--26:5}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-315-7}, ISSN = {1868-8969}, year = {2024}, volume = {292}, editor = {Casteigts, Arnaud and Kuhn, Fabian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.26}, URN = {urn:nbn:de:0030-drops-199044}, doi = {10.4230/LIPIcs.SAND.2024.26}, annote = {Keywords: Modular robots, Collision detection, Computational Geometry, Complexity} }

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Complete Volume

**Published in:** LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

LIPIcs, Volume 221, SAND 2022, Complete Volume

1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 1-370, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{aspnes_et_al:LIPIcs.SAND.2022, title = {{LIPIcs, Volume 221, SAND 2022, Complete Volume}}, booktitle = {1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)}, pages = {1--370}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-224-2}, ISSN = {1868-8969}, year = {2022}, volume = {221}, editor = {Aspnes, James and Michail, Othon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022}, URN = {urn:nbn:de:0030-drops-159412}, doi = {10.4230/LIPIcs.SAND.2022}, annote = {Keywords: LIPIcs, Volume 221, SAND 2022, Complete Volume} }

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Front Matter

**Published in:** LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Front Matter, Table of Contents, Preface, Conference Organization

1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{aspnes_et_al:LIPIcs.SAND.2022.0, author = {Aspnes, James and Michail, Othon}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)}, pages = {0:i--0:xvi}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-224-2}, ISSN = {1868-8969}, year = {2022}, volume = {221}, editor = {Aspnes, James and Michail, Othon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.0}, URN = {urn:nbn:de:0030-drops-159426}, doi = {10.4230/LIPIcs.SAND.2022.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

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Brief Announcement

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

We study population protocols: networks of anonymous agents whose pairwise interactions are chosen uniformly at random. The size counting problem is that of calculating the exact number n of agents in the population, assuming no leader (each agent starts in the same state). We give the first protocol that solves this problem in sublinear time.
The protocol converges in O(log n log log n) time and uses O(n^60) states (O(1) + 60 log n bits of memory per agent) with probability 1-O((log log n)/n). The time to converge is also O(log n log log n) in expectation. Crucially, unlike most published protocols with omega(1) states, our protocol is uniform: it uses the same transition algorithm for any population size, so does not need an estimate of the population size to be embedded into the algorithm.

David Doty, Mahsa Eftekhari, Othon Michail, Paul G. Spirakis, and Michail Theofilatos. Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 46:1-46:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{doty_et_al:LIPIcs.DISC.2018.46, author = {Doty, David and Eftekhari, Mahsa and Michail, Othon and Spirakis, Paul G. and Theofilatos, Michail}, title = {{Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {46:1--46:3}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.46}, URN = {urn:nbn:de:0030-drops-98359}, doi = {10.4230/LIPIcs.DISC.2018.46}, annote = {Keywords: population protocol, counting, leader election, polylogarithmic time} }

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**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

In this work, we study theoretical models of programmable matter systems. The systems under consideration consist of spherical modules, kept together by magnetic forces and able to perform two minimal mechanical operations (or movements): rotate around a neighbor and slide over a line. In terms of modeling, there are n nodes arranged in a 2-dimensional grid and forming some initial shape. The goal is for the initial shape A to transform to some target shape B by a sequence of movements. Most of the paper focuses on transformability questions, meaning whether it is in principle feasible to transform a given shape to another. We first consider the case in which only rotation is available to the nodes. Our main result is that deciding whether two given shapes A and B can be transformed to each other is in P. We then insist on rotation only and impose the restriction that the nodes must maintain global connectivity throughout the transformation. We prove that the corresponding transformability question is in PSPACE and study the problem of determining the minimum seeds that can make feasible otherwise infeasible transformations. Next we allow both rotations and slidings and prove universality: any two connected shapes A,B of the same number of nodes, can be transformed to each other without breaking connectivity. The worst-case number of movements of the generic strategy is Theta(n^2). We improve this to O(n) parallel time, by a pipelining strategy, and prove optimality of both by matching lower bounds. We next turn our attention to distributed transformations. The nodes are now distributed processes able to perform communicate-compute-move rounds. We provide distributed algorithms for a general type of transformation.

Othon Michail, George Skretas, and Paul G. Spirakis. On the Transformation Capability of Feasible Mechanisms for Programmable Matter. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 136:1-136:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{michail_et_al:LIPIcs.ICALP.2017.136, author = {Michail, Othon and Skretas, George and Spirakis, Paul G.}, title = {{On the Transformation Capability of Feasible Mechanisms for Programmable Matter}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {136:1--136:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.136}, URN = {urn:nbn:de:0030-drops-74341}, doi = {10.4230/LIPIcs.ICALP.2017.136}, annote = {Keywords: programmable matter, transformation, reconfigurable robotics, shape formation, complexity, distributed algorithms} }

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

We propose a novel, generic definition of emph{probabilistic schedulers} for population protocols. We design two new schedulers, the emph{State Scheduler} and the emph{Transition Function Scheduler}. Both possess the significant capability of being emph{protocol-aware}, i.e. they can assign transition probabilities based on information concerning the underlying protocol. We prove that the proposed schedulers, and also the emph{Random Scheduler} that was defined by Angluin et al. cite{AADFP04}, are all fair with probability $1$. We also define and study emph{equivalence} between schedulers w.r.t. emph{performance} and emph{correctness} and prove that there exist fair probabilistic schedulers that are not equivalent w.r.t. to performance and others that are not equivalent w.r.t. correctness. We implement our schedulers using a new tool for simulating population protocols and evaluate their performance from the viewpoint of experimental analysis and verification. We study three representative protocols to verify stability, and compare the experimental time to convergence with the known complexity bounds. We run our experiments from very small to extremely large populations (of up to $10^{8}$ agents). We get very promising results both of theoretical and practical interest.

Ioannis Chatzigiannakis, Shlomi Dolev, Sándor Fekete, Othon Michail, and Paul Spirakis. On the Fairness of Probabilistic Schedulers for Population Protocols. In Algorithmic Methods for Distributed Cooperative Systems. Dagstuhl Seminar Proceedings, Volume 9371, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chatzigiannakis_et_al:DagSemProc.09371.4, author = {Chatzigiannakis, Ioannis and Dolev, Shlomi and Fekete, S\'{a}ndor and Michail, Othon and Spirakis, Paul}, title = {{On the Fairness of Probabilistic Schedulers for Population Protocols}}, booktitle = {Algorithmic Methods for Distributed Cooperative Systems}, pages = {1--23}, 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.09371.4}, URN = {urn:nbn:de:0030-drops-24286}, doi = {10.4230/DagSemProc.09371.4}, annote = {Keywords: Population Protocols, Fairness, Probabilistic Schedulers, Communicating Automata, Sensor Networks, Experimental Evaluation} }