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**Published in:** LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

We develop a framework for self-induced phase changes in programmable matter in which a collection of agents with limited computational and communication capabilities can collectively perform appropriate global tasks in response to local stimuli that dynamically appear and disappear. Agents reside on graph vertices, where each stimulus is only recognized locally, and agents communicate via token passing along edges to alert other agents to transition to an Aware state when stimuli are present and an Unaware state when the stimuli disappear. We present an Adaptive Stimuli Algorithm that is robust to competing waves of messages as multiple stimuli change, possibly adversarially. Moreover, in addition to handling arbitrary stimulus dynamics, the algorithm can handle agents reconfiguring the connections (edges) of the graph over time in a controlled way.
As an application, we show how this Adaptive Stimuli Algorithm on reconfigurable graphs can be used to solve the foraging problem, where food sources may be discovered, removed, or shifted at arbitrary times. We would like the agents to consistently self-organize, using only local interactions, such that if the food remains in a position long enough, the agents transition to a gather phase in which many collectively form a single large component with small perimeter around the food. Alternatively, if no food source has existed recently, the agents should undergo a self-induced phase change and switch to a search phase in which they distribute themselves randomly throughout the lattice region to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable, withstanding competing waves of messages that may interfere with each other. Like a physical phase change, microscopic changes such as the deletion or addition of a single food source trigger these macroscopic, system-wide transitions as agents share information about the environment and respond locally to get the desired collective response.

Shunhao Oh, Dana Randall, and Andréa W. Richa. Adaptive Collective Responses to Local Stimuli in Anonymous Dynamic Networks. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{oh_et_al:LIPIcs.SAND.2023.6, author = {Oh, Shunhao and Randall, Dana and Richa, Andr\'{e}a W.}, title = {{Adaptive Collective Responses to Local Stimuli in Anonymous Dynamic Networks}}, booktitle = {2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)}, pages = {6:1--6:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-275-4}, ISSN = {1868-8969}, year = {2023}, volume = {257}, editor = {Doty, David and Spirakis, Paul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.6}, URN = {urn:nbn:de:0030-drops-179424}, doi = {10.4230/LIPIcs.SAND.2023.6}, annote = {Keywords: Dynamic networks, adaptive stimuli, foraging, self-organizing particle systems, programmable matter} }

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Brief Announcement

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

The foraging problem asks how a collective of particles with limited computational, communication and movement capabilities can autonomously compress around a food source and disperse when the food is depleted or shifted, which may occur at arbitrary times. We would like the particles to iteratively self-organize, using only local interactions, to correctly gather whenever a food particle remains in a position long enough and search if no food particle has existed recently. Unlike previous approaches, these search and gather phases should be self-induced so as to be indefinitely repeatable as the food evolves, with microscopic changes to the food triggering macroscopic, system-wide phase transitions. We present a stochastic foraging algorithm based on a phase change in the fixed magnetization Ising model from statistical physics: Our algorithm is the first to leverage self-induced phase changes as an algorithmic tool. A key component of our algorithm is a careful token passing mechanism ensuring a dispersion broadcast wave will always outpace a compression wave.

Shunhao Oh, Dana Randall, and Andréa W. Richa. Brief Announcement: Foraging in Particle Systems via Self-Induced Phase Changes. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 51:1-51:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{oh_et_al:LIPIcs.DISC.2022.51, author = {Oh, Shunhao and Randall, Dana and Richa, Andr\'{e}a W.}, title = {{Brief Announcement: Foraging in Particle Systems via Self-Induced Phase Changes}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {51:1--51:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.51}, URN = {urn:nbn:de:0030-drops-172423}, doi = {10.4230/LIPIcs.DISC.2022.51}, annote = {Keywords: Foraging, self-organized particle systems, compression, phase changes} }

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RANDOM

**Published in:** LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

We present local distributed, stochastic algorithms for alignment in self-organizing particle systems (SOPS) on two-dimensional lattices, where particles occupy unique sites on the lattice, and particles can make spatial moves to neighboring sites if they are unoccupied. Such models are abstractions of programmable matter, composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational capabilities. We consider oriented particle systems, where particles are assigned a vector pointing in one of q directions, and each particle can compute the angle between its direction and the direction of any neighboring particle, although without knowledge of global orientation with respect to a fixed underlying coordinate system. Particles move stochastically, with each particle able to either modify its direction or make a local spatial move along a lattice edge during a move. We consider two settings: (a) where particle configurations must remain simply connected at all times and (b) where spatial moves are unconstrained and configurations can disconnect.
Our algorithms are inspired by the Potts model and its planar oriented variant known as the planar Potts model or clock model from statistical physics. We prove that for any q ≥ 2, by adjusting a single parameter, these self-organizing particle systems can be made to collectively align along a single dominant direction (analogous to a solid or ordered state) or remain non-aligned, in which case the fraction of particles oriented along any direction is nearly equal (analogous to a gaseous or disordered state). In the connected SOPS setting, we allow for two distinct parameters, one controlling the ferromagnetic attraction between neighboring particles (regardless of orientation) and the other controlling the preference of neighboring particles to align. We show that with appropriate settings of the input parameters, we can achieve compression and expansion, controlling how tightly gathered the particles are, as well as alignment or nonalignment, producing a single dominant orientation or not. While alignment is known for the Potts and clock models at sufficiently low temperatures, our proof in the SOPS setting are significantly more challenging because the particles make spatial moves, not all sites are occupied, and the total number of particles is fixed.

Hridesh Kedia, Shunhao Oh, and Dana Randall. Local Stochastic Algorithms for Alignment in Self-Organizing Particle Systems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kedia_et_al:LIPIcs.APPROX/RANDOM.2022.14, author = {Kedia, Hridesh and Oh, Shunhao and Randall, Dana}, title = {{Local Stochastic Algorithms for Alignment in Self-Organizing Particle Systems}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)}, pages = {14:1--14:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-249-5}, ISSN = {1868-8969}, year = {2022}, volume = {245}, editor = {Chakrabarti, Amit and Swamy, Chaitanya}, 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.2022.14}, URN = {urn:nbn:de:0030-drops-171367}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.14}, annote = {Keywords: Self-organizing particle systems, alignment, Markov chains, active matter} }

Document

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)

Bandit-style algorithms have been studied extensively in stochastic and adversarial settings. Such algorithms have been shown to be useful in multiplayer settings, e.g. to solve the wireless network selection problem, which can be formulated as an adversarial bandit problem. A leading bandit algorithm for the adversarial setting is EXP3. However, network behavior is often repetitive, where user density and network behavior follow regular patterns. Bandit algorithms, like EXP3, fail to provide good guarantees for periodic behaviors. A major reason is that these algorithms compete against fixed-action policies, which is ineffective in a periodic setting.
In this paper, we define a periodic bandit setting, and periodic regret as a better performance measure for this type of setting. Instead of comparing an algorithm’s performance to fixed-action policies, we aim to be competitive with policies that play arms under some set of possible periodic patterns F (for example, all possible periodic functions with periods 1,2,*s,P). We propose Periodic EXP4, a computationally efficient variant of the EXP4 algorithm for periodic settings. With K arms, T time steps, and where each periodic pattern in F is of length at most P, we show that the periodic regret obtained by Periodic EXP4 is at most O(sqrt{PKT log K + KT log |F|}). We also prove a lower bound of Omega (sqrt{PKT + KT {log |F|}/{log K}}) for the periodic setting, showing that this is optimal within log-factors. As an example, we focus on the wireless network selection problem. Through simulation, we show that Periodic EXP4 learns the periodic pattern over time, adapts to changes in a dynamic environment, and far outperforms EXP3.

Shunhao Oh, Anuja Meetoo Appavoo, and Seth Gilbert. Periodic Bandits and Wireless Network Selection. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 149:1-149:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{oh_et_al:LIPIcs.ICALP.2019.149, author = {Oh, Shunhao and Appavoo, Anuja Meetoo and Gilbert, Seth}, title = {{Periodic Bandits and Wireless Network Selection}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {149:1--149:15}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.149}, URN = {urn:nbn:de:0030-drops-107251}, doi = {10.4230/LIPIcs.ICALP.2019.149}, annote = {Keywords: multi-armed bandits, wireless network selection, periodicity in environment} }

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