Joshua J. Daymude

Garrett Parzych, Joshua J. Daymude

We introduce the problem of adaptive self-organization in which the nodes of an anonymous, synchronous dynamic network must distributively change the collective distribution of their responses (or "colors") as a function of time-varying environmental signals, even when these signals are only perceived locally and the network topology changes adversarially. Specifically, a signal adversary may change the type of signal and which node(s) witness that signal arbitrarily between rounds. If a signal (or lack thereof) $s$ persists in the system for sufficiently long, the dynamic network must stabilize such that nodes' colors reach and remain in a distribution closely approximating $r(s)$, a goal distribution defined by the problem instance. We first prove that if nodes are deterministic, the only solvable instances of adaptive-self organization are those with homogeneous goal distributions, i.e., those where all nodes must stabilize with the same color. We then present a linear-time, logarithmic-memory, deterministic algorithm for this subclass of instances that works even when the multiplicity and location of signal witnesses change arbitrarily. When nodes know $n$, the number of nodes in the network, a small adaptation of this algorithm achieves a stronger convergence property in which adversarial edge and signal dynamics are entirely unable to disturb stabilized configurations. Finally, we present a randomized extension of these algorithms that solves arbitrary (i.e., not necessarily homogeneous) instances of adaptive self-organization with high probability when nodes know the goal distributions.

Joshua J. Daymude, Antonio M. Espinoza, Holly Bergen et al.

The battle for a more secure Internet is waged on many fronts, including the most basic of networking protocols. Our focus is the IPv4 Identifier (IPID), an IPv4 header field as old as the Internet with an equally long history as an exploited side channel for scanning network properties, inferring off-path connections, and poisoning DNS caches. This article taxonomizes the 25-year history of IPID-based exploits and the corresponding changes to IPID selection methods. By mathematically analyzing these methods' correctness and security and empirically evaluating their performance, we reveal recommendations for best practice as well as shortcomings of current operating system implementations, emphasizing the value of systematic evaluations in network security.

Joshua J. Daymude, Robert Axelrod, Stephanie Forrest

Expressions of dissent against authority are an important feature of most societies, and efforts to suppress such expressions are common. Modern digital communications, social media, and Internet surveillance and censorship technologies are changing the landscape of public speech and dissent. Especially in authoritarian settings, individuals must assess the risk of voicing their true opinions or choose self-censorship, voluntarily moderating their behavior to comply with authority. We present a model in which individuals strategically manage the tradeoff between expressing dissent and avoiding punishment through self-censorship while an authority adapts its policies to minimize both total expressed dissent and punishment costs. We study the model analytically and in simulation to derive conditions separating defiant individuals who express their desired dissent in spite of punishment from self-censoring individuals who fully or partially limit their expression. We find that for any population, there exists an authority policy that leads to total self-censorship. However, the probability and time for an initially moderate, locally-adaptive authority to suppress dissent depend critically on the population's willingness to withstand punishment early on, which can deter the authority from adopting more extreme policies.

Devendra Parkar, Anya Chaturvedi, Joshua J. Daymude

We present the first unsupervised learning model for finding Maximum Independent Sets (MaxIS) in dynamic graphs where edges change over time. Our method combines structural learning from graph neural networks (GNNs) with a learned distributed update mechanism that, given an edge addition or deletion event, modifies nodes' internal memories and infers their MaxIS membership in a single, parallel step. We parameterize our model by the update mechanism's radius and investigate the resulting performance-runtime tradeoffs for various dynamic graph topologies. We evaluate our model against a mixed integer programming solver and the state-of-the-art learning-based methods for MaxIS on static graphs (ICML 2020; NeurIPS 2020, 2023). Across synthetic and empirical dynamic graphs of 50-1,000 nodes, our model achieves competitive approximation ratios with excellent scalability; on large graphs, it significantly outperforms the state-of-the-art learning methods in solution quality, runtime, and memory usage. When generalizing to graphs of 10,000 nodes (100x larger than the ones used for training), our model produces MaxIS solutions 1.05-1.18x larger than any other learning method, even while maintaining competitive runtimes.

Anya Chaturvedi, Joshua J. Daymude, Andréa W. Richa

Algorithms for mutual exclusion aim to isolate potentially concurrent accesses to the same shared resources. Motivated by distributed computing research on programmable matter and population protocols where interactions among entities are often assumed to be isolated, Daymude, Richa, and Scheideler (SAND`22) introduced a variant of the local mutual exclusion problem that applies to arbitrary dynamic networks: each node, on issuing a lock request, must acquire exclusive locks on itself and all its persistent neighbors, i.e., the neighbors that remain connected to it over the duration of the lock request. Assuming adversarial edge dynamics, semi-synchronous or asynchronous concurrency, and anonymous nodes communicating via message passing, their randomized algorithm achieves mutual exclusion (non-intersecting lock sets) and lockout freedom (eventual success with probability 1). However, they did not analyze their algorithm's runtime. In this paper, we prove that any node will successfully lock itself and its persistent neighbors within O$(nΔ^3)$ open rounds of its lock request in expectation, where $n$ is the number of nodes in the dynamic network, $Δ$ is the maximum degree of the dynamic network, rounds are normalized to the execution time of the ``slowest'' node, and ``closed'' rounds when some persistent neighbors are already locked by another node are ignored (i.e., only ``open" rounds are considered).

Garrett Parzych, Joshua J. Daymude

Broadcast is a ubiquitous distributed computing problem that underpins many other system tasks. In static, connected networks, it was recently shown that broadcast is solvable without any node memory and only constant-size messages in worst-case asymptotically optimal time (Hussak and Trehan, PODC'19/STACS'20/DC'23). In the dynamic setting of adversarial topology changes, however, existing algorithms rely on identifiers, port labels, or polynomial memory to solve broadcast and compute functions over node inputs. We investigate space-efficient, terminating broadcast algorithms for anonymous, synchronous, 1-interval connected dynamic networks and introduce the first memory lower bounds in this setting. Specifically, we prove that broadcast with termination detection is impossible for idle-start algorithms (where only the broadcaster can initially send messages) and otherwise requires $Ω(\log n)$ memory per node, where $n$ is the number of nodes in the network. Even if the termination condition is relaxed to stabilizing termination (eventually no additional messages are sent), we show that any idle-start algorithm must use $ω(1)$ memory per node, separating the static and dynamic settings for anonymous broadcast. This lower bound is not far from optimal, as we present an algorithm that solves broadcast with stabilizing termination using $\mathcal{O}(\log n)$ memory per node in worst-case asymptotically optimal time. In sum, these results reveal the necessity of non-constant memory for nontrivial terminating computation in anonymous dynamic networks.

Devendra Parkar, Kirtus G. Leyba, Raylene A. Faerber et al.

Local interactions drive emergent collective behavior, which pervades biological and social complex systems. But uncovering the interactions that produce a desired behavior remains a core challenge. In this paper, we present EvoSOPS, an evolutionary framework that searches landscapes of stochastic distributed algorithms for those that achieve a mathematically specified target behavior. These algorithms govern self-organizing particle systems (SOPS) comprising individuals with no persistent memory and strictly local sensing and movement. For aggregation, phototaxing, and separation behaviors, EvoSOPS discovers algorithms that achieve 4.2-15.3% higher fitness than those from the existing "stochastic approach to SOPS" based on mathematical theory from statistical physics. EvoSOPS is also flexibly applied to new behaviors such as object coating where the stochastic approach would require bespoke, extensive analysis. Finally, we distill insights from the diverse, best-fitness genomes produced for aggregation across repeated EvoSOPS runs to demonstrate how EvoSOPS can bootstrap future theoretical investigations into SOPS algorithms for new behaviors.

Jamison W. Weber, Tishya Chhabra, Andréa W. Richa et al.

Individual modules of programmable matter participate in their system's collective behavior by expending energy to perform actions. However, not all modules may have access to the external energy source powering the system, necessitating a local and distributed strategy for supplying energy to modules. In this work, we present a general energy distribution framework for the canonical amoebot model of programmable matter that transforms energy-agnostic algorithms into energy-constrained ones with equivalent behavior and an $\mathcal{O}(n^2)$-round runtime overhead -- even under an unfair adversary -- provided the original algorithms satisfy certain conventions. We then prove that existing amoebot algorithms for leader election (ICDCN 2023) and shape formation (Distributed Computing, 2023) are compatible with this framework and show simulations of their energy-constrained counterparts, demonstrating how other unfair algorithms can be generalized to the energy-constrained setting with relatively little effort. Finally, we show that our energy distribution framework can be composed with the concurrency control framework for amoebot algorithms (Distributed Computing, 2023), allowing algorithm designers to focus on the simpler energy-agnostic, sequential setting but gain the general applicability of energy-constrained, asynchronous correctness.

Joseph L. Briones, Tishya Chhabra, Joshua J. Daymude et al.

Over three decades of scientific endeavors to realize programmable matter, a substance that can change its physical properties based on user input or responses to its environment, there have been many advances in both the engineering of modular robotic systems and the corresponding algorithmic theory of collective behavior. However, while the design of modular robots routinely addresses the challenges of realistic three-dimensional (3D) space, algorithmic theory remains largely focused on 2D abstractions such as planes and planar graphs. In this work, we formalize the 3D geometric space variant for the canonical amoebot model of programmable matter, using the face-centered cubic (FCC) lattice to represent space and define local spatial orientations. We then give a distributed algorithm for leader election in connected, contractible 2D or 3D geometric amoebot systems that deterministically elects exactly one leader in $\mathcal{O}(n)$ rounds under an unfair sequential adversary, where $n$ is the number of amoebots in the system. We then demonstrate how this algorithm can be transformed using the concurrency control framework for amoebot algorithms (DISC 2021) to obtain the first known amoebot algorithm, both in 2D and 3D space, to solve leader election under an unfair asynchronous adversary.

Joshua J. Daymude, Andréa W. Richa, Christian Scheideler

Mutual exclusion is a classical problem in distributed computing that provides isolation among concurrent action executions that may require access to the same shared resources. Inspired by algorithmic research on distributed systems of weakly capable entities whose connections change over time, we address the local mutual exclusion problem that tasks each node with acquiring exclusive locks for itself and the maximal subset of its "persistent" neighbors that remain connected to it over the time interval of the lock request. Using the established time-varying graphs model to capture adversarial topological changes, we propose and rigorously analyze a local mutual exclusion algorithm for nodes that are anonymous and communicate via asynchronous message passing. The algorithm satisfies mutual exclusion (non-intersecting lock sets) and lockout freedom (eventual success with probability 1) under both semi-synchronous and asynchronous concurrency. It requires $\mathcal{O}(Δ)$ memory per node and messages of size $Θ(1)$, where $Δ$ is the maximum number of connections per node. We conclude by describing how our algorithm can implement the pairwise interactions assumed by population protocols and the concurrency control operations assumed by the canonical amoebot model, demonstrating its utility in both passively and actively dynamic distributed systems.

Kirtus G. Leyba, Joshua J. Daymude, Jean-Gabriel Young et al.

The Border Gateway Protocol (BGP) is a distributed protocol that manages interdomain routing without requiring a centralized record of which autonomous systems (ASes) connect to which others. Many methods have been devised to infer the AS topology from publicly available BGP data, but none provide a general way to handle the fact that the data are notoriously incomplete and subject to error. This paper describes a method for reliably inferring AS-level connectivity in the presence of measurement error using Bayesian statistical inference acting on BGP routing tables from multiple vantage points. We employ a novel approach for counting AS adjacency observations in the AS-PATH attribute data from public route collectors, along with a Bayesian algorithm to generate a statistical estimate of the AS-level network. Our approach also gives us a way to evaluate the accuracy of existing reconstruction methods and to identify advantageous locations for new route collectors or vantage points.

Joshua J. Daymude, Noble C. Harasha, Andréa W. Richa et al.

Aggregation is a fundamental behavior for swarm robotics that requires a system to gather together in a compact, connected cluster. In 2014, Gauci et al. proposed a surprising algorithm that reliably achieves swarm aggregation using only a binary line-of-sight sensor and no arithmetic computation or persistent memory. It has been rigorously proven that this algorithm will aggregate one robot to another, but it remained open whether it would always aggregate a system of $n > 2$ robots as was observed in experiments and simulations. We prove that there exist deadlocked configurations from which this algorithm cannot achieve aggregation for $n > 3$ robots when the robots' motion is uniform and deterministic. On the positive side, we show that the algorithm (i) is robust to small amounts of error, enabling deadlock avoidance, and (ii) provably achieves a linear runtime speedup for the $n = 2$ case when using a cone-of-sight sensor. Finally, we introduce a noisy, discrete adaptation of this algorithm that is more amenable to rigorous analysis of noise and whose simulation results align qualitatively with the original, continuous algorithm.

Joshua J. Daymude, Andréa W. Richa, Christian Scheideler

The amoebot model abstracts active programmable matter as a collection of simple computational elements called amoebots that interact locally to collectively achieve tasks of coordination and movement. Since its introduction at SPAA 2014, a growing body of literature has adapted its assumptions for a variety of problems; however, without a standardized hierarchy of assumptions, precise systematic comparison of results under the amoebot model is difficult. We propose the canonical amoebot model, an updated formalization that distinguishes between core model features and families of assumption variants. A key improvement addressed by the canonical amoebot model is concurrency. Much of the existing literature implicitly assumes amoebot actions are isolated and reliable, reducing analysis to the sequential setting where at most one amoebot is active at a time. However, real programmable matter systems are concurrent. The canonical amoebot model formalizes all amoebot communication as message passing, leveraging adversarial activation models of concurrent executions. Under this granular treatment of time, we take two complementary approaches to concurrent algorithm design. We first establish a set of sufficient conditions for algorithm correctness under any concurrent execution, embedding concurrency control directly in algorithm design. We then present a concurrency control framework that uses locks to convert amoebot algorithms that terminate in the sequential setting and satisfy certain conventions into algorithms that exhibit equivalent behavior in the concurrent setting. As a case study, we demonstrate both approaches using a simple algorithm for hexagon formation. Together, the canonical amoebot model and these complementary approaches to concurrent algorithm design open new directions for distributed computing research on programmable matter.

Shengkai Li, Bahnisikha Dutta, Sarah Cannon et al.

Active matter physics and swarm robotics have provided powerful tools for the study and control of ensembles driven by internal sources. At the macroscale, controlling swarms typically utilizes significant memory, processing power, and coordination unavailable at the microscale, e.g., for colloidal robots, which could be useful for fighting disease, fabricating intelligent textiles, and designing nanocomputers. To develop principles that that can leverage physics of interactions and thus can be utilized across scales, we take a two-pronged approach: a theoretical abstraction of self-organizing particle systems and an experimental robot system of active cohesive granular matter that intentionally lacks digital electronic computation and communication, using minimal (or no) sensing and control, to test theoretical predictions. We consider the problems of aggregation, dispersion, and collective transport. As predicted by the theory, as a parameter representing interparticle attraction increases, the robots transition from a dispersed phase to an aggregated one, forming a dense, compact collective. When aggregated, the collective can transport non-robot "impurities" in their environment, thus performing an emergent task driven by the physics underlying the transition. These results point to a fruitful interplay between algorithm design and active matter robophysics that can result in new nonequilibrium physics and principles for programming collectives without the need for complex algorithms or capabilities.

Joshua J. Daymude, Andréa W. Richa, Jamison W. Weber

In systems of active programmable matter, individual modules require a constant supply of energy to participate in the system's collective behavior. These systems are often powered by an external energy source accessible by at least one module and rely on module-to-module power transfer to distribute energy throughout the system. While much effort has gone into addressing challenging aspects of power management in programmable matter hardware, algorithmic theory for programmable matter has largely ignored the impact of energy usage and distribution on algorithm feasibility and efficiency. In this work, we present an algorithm for energy distribution in the amoebot model that is loosely inspired by the growth behavior of Bacillus subtilis bacterial biofilms. These bacteria use chemical signaling to communicate their metabolic states and regulate nutrient consumption throughout the biofilm, ensuring that all bacteria receive the nutrients they need. Our algorithm similarly uses communication to inhibit energy usage when there are starving modules, enabling all modules to receive sufficient energy to meet their demands. As a supporting but independent result, we extend the amoebot model's well-established spanning forest primitive so that it self-stabilizes in the presence of crash failures. We conclude by showing how this self-stabilizing primitive can be leveraged to compose our energy distribution algorithm with existing amoebot model algorithms, effectively generalizing previous work to also consider energy constraints.

Joshua J. Daymude, Robert Gmyr, Kristian Hinnenthal et al.

We envision programmable matter as a system of nano-scale agents (called particles) with very limited computational capabilities that move and compute collectively to achieve a desired goal. We use the geometric amoebot model as our computational framework, which assumes particles move on the triangular lattice. Motivated by the problem of sealing an object using minimal resources, we show how a particle system can self-organize to form an object's convex hull. We give a distributed, local algorithm for convex hull formation and prove that it runs in $\mathcal{O}(B)$ asynchronous rounds, where $B$ is the length of the object's boundary. Within the same asymptotic runtime, this algorithm can be extended to also form the object's (weak) $\mathcal{O}$-hull, which uses the same number of particles but minimizes the area enclosed by the hull. Our algorithms are the first to compute convex hulls with distributed entities that have strictly local sensing, constant-size memory, and no shared sense of orientation or coordinates. Ours is also the first distributed approach to computing restricted-orientation convex hulls. This approach involves coordinating particles as distributed memory; thus, as a supporting but independent result, we present and analyze an algorithm for organizing particles with constant-size memory as distributed binary counters that efficiently support increments, decrements, and zero-tests --- even as the particles move.

John Calvin Alumbaugh, Joshua J. Daymude, Erik D. Demaine et al.

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA) model was recently introduced as a platform to help study connections between various models of self-assembly. However, in this paper we present a result in which we use TA to simulate arbitrary systems within the amoebot model, a theoretical model of programmable matter in which the individual components are relatively simple state machines that are able to sense the states of their neighbors and to move via series of expansions and contractions. We show that for every amoebot system, there is a TA system capable of simulating the local information transmission built into amoebot particles, and that the TA "macrotiles" used to simulate its particles are capable of simulating movement (via attachment and detachment operations) while maintaining the necessary properties of amoebot particle systems. The TA systems are able to utilize only the local interactions of state changes and binding and unbinding along tile edges, but are able to fully simulate the dynamics of these programmable matter systems.

Sarah Cannon, Joshua J. Daymude, Cem Gokmen et al.

We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational power. We consider heterogeneous particle systems of two different colors and prove that these systems can collectively separate into different color classes or integrate, indifferent to color. We accomplish both behaviors with the same fully distributed, local, stochastic algorithm. Achieving separation or integration depends only on a single global parameter determining whether particles prefer to be next to other particles of the same color or not; this parameter is meant to represent external, environmental influences on the particle system. The algorithm is a generalization of a previous distributed, stochastic algorithm for compression (PODC '16), which can be viewed as a special case of separation where all particles have the same color. It is significantly more challenging to prove that the desired behavior is achieved in the heterogeneous setting, however, even in the bichromatic case we focus on. This requires combining several new techniques, including the cluster expansion from statistical physics, a new variant of the bridging argument of Miracle, Pascoe and Randall (RANDOM '11), the high-temperature expansion of the Ising model, and careful probabilistic arguments.

Sarah Cannon, Joshua J. Daymude, William Savoie et al.

Smarticles, or smart active particles, are small robots equipped with only basic movement and sensing abilities that are incapable of rotating or displacing individually. We study the ensemble behavior of smarticles, i.e., the behavior a collective of these very simple computational elements can achieve, and how such behavior can be implemented using minimal programming. We show that an ensemble of smarticles constrained to remain close to one another (which we call a supersmarticle), achieves directed locomotion toward or away from a light source, a phenomenon known as phototaxing. We present experimental and theoretical models of phototactic supersmarticles that collectively move with a directed displacement in response to light. The motion of the supersmarticle is approximately Brownian, and is a result of chaotic interactions among smarticles. The system can be directed by introducing asymmetries among the individual smarticle's behavior, in our case by varying activity levels in response to light, resulting in supersmarticle biased motion.

Joshua J. Daymude, Robert Gmyr, Andrea W. Richa et al.

We consider programmable matter that consists of computationally limited devices (called particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention. We use the geometric amoebot model to describe such self-organizing particle systems, which defines how particles can actively move and communicate with one another. In this paper, we present an efficient local-control algorithm which solves the leader election problem in O(n) asynchronous rounds with high probability, where n is the number of particles in the system. Our algorithm relies only on local information --- particles do not have unique identifiers, any knowledge of n, or any sort of global coordinate system --- and requires only constant memory per particle.