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Today’s mainstream network timing models for distributed computing are synchrony, partial synchrony, and asynchrony. These models are coarse-grained and often make either too strong or too weak assumptions about the network. This paper introduces a new timing model called granular synchrony that models the network as a mixture of synchronous, partially synchronous, and asynchronous communication links. The new model is not only theoretically interesting but also more representative of real-world networks. It also serves as a unifying framework where current mainstream models are its special cases. We present necessary and sufficient conditions for solving crash and Byzantine fault-tolerant consensus in granular synchrony. Interestingly, consensus among n parties can be achieved against f ≥ n/2 crash faults or f ≥ n/3 Byzantine faults without resorting to full synchrony. 

Local interactions of uncoordinated individuals produce the collective behaviors of many biological systems, inspiring much of the current research in programmable matter. A striking example is the spontaneous assembly of fire ants into "bridges" comprising their own bodies to traverse obstacles and reach sources of food. Experiments and simulations suggest that, remarkably, these ants always form one bridge - instead of multiple, competing bridges - despite a lack of central coordination. We argue that the reliable formation of a single bridge does not require sophistication on behalf of the individuals by provably reproducing this behavior in a self-organizing particle system. We show that the formation of a single bridge by the particles is a statistical inevitability of their preferences to move in a particular direction, such as toward a food source, and their preference for more neighbors. Two parameters, η and β, reflect the strengths of these preferences and determine the Gibbs stationary measure of the corresponding particle system’s Markov chain dynamics. We show that a single bridge almost certainly forms when η and β are sufficiently large. Our proof introduces an auxiliary Markov chain, called an "occupancy chain," that captures only the significant, global changes to the system. Through the occupancy chain, we abstract away information about the motion of individual particles, but we gain a more direct means of analyzing their collective behavior. Such abstractions provide a promising new direction for understanding many other systems of programmable matter. 

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 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. 

Chemical reaction networks (CRNs) model systems where molecules interact according to a finite set of reactions such as A + B → C, representing that if a molecule of A and B collide, they disappear and a molecule of C is produced. CRNs can compute Boolean-valued predicates ϕ:ℕ^d → {0,1} and integer-valued functions f:ℕ^d → ℕ; for instance X₁ + X₂ → Y computes the function min(x₁,x₂), since starting with x_i copies of X_i, eventually min(x₁,x₂) copies of Y are produced. We study the computational power of execution bounded CRNs, in which only a finite number of reactions can occur from the initial configuration (e.g., ruling out reversible reactions such as A ⇌ B). The power and composability of such CRNs depend crucially on some other modeling choices that do not affect the computational power of CRNs with unbounded executions, namely whether an initial leader is present, and whether (for predicates) all species are required to "vote" for the Boolean output. If the CRN starts with an initial leader, and can allow only the leader to vote, then all semilinear predicates and functions can be stably computed in O(n log n) parallel time by execution bounded CRNs. However, if no initial leader is allowed, all species vote, and the CRN is "non-collapsing" (does not shrink from initially large to final O(1) size configurations), then execution bounded CRNs are severely limited, able to compute only eventually constant predicates. A key tool is a characterization of execution bounded CRNs as precisely those with a nonnegative linear potential function that is strictly decreased by every reaction [Czerner et al., 2024]. 

We provide a fast distributed algorithm for detecting h-cycles in the Congested Clique model, whose running time decreases as the number of h-cycles in the graph increases. In undirected graphs, constant-round algorithms are known for cycles of even length. Our algorithm greatly improves upon the state of the art for odd values of h. Moreover, our running time applies also to directed graphs, in which case the improvement is for all values of h. Further, our techniques allow us to obtain a triangle detection algorithm in the quantum variant of this model, which is faster than prior work. A key technical contribution we develop to obtain our fast cycle detection algorithm is a new algorithm for computing the product of many pairs of small matrices in parallel, which may be of independent interest. 

The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an O(log Δ)-approximation (where Δ is the maximum set size) and an O(f)-approximation (where f is the maximum number of sets containing any given element). In this paper, we introduce a new, surprisingly simple, model-independent approach to solving SetCover in unweighted graphs. We obtain multiple improved algorithms in the MPC and CRCW PRAM models. First, in the MPC model with sublinear space per machine, our algorithms can compute an O(f) approximation to SetCover in Ô(√{log Δ} + log f) rounds and a O(log Δ) approximation in O(log^{3/2} n) rounds. Moreover, in the PRAM model, we give a O(f) approximate algorithm using linear work and O(log n) depth. All these bounds improve the existing round complexity/depth bounds by a log^{Ω(1)} n factor. Moreover, our approach leads to many other new algorithms, including improved algorithms for the HypergraphMatching problem in the MPC model, as well as simpler SetCover algorithms that match the existing bounds. 

In contrast to proof-of-work replication, Byzantine quorum systems maintain consistency across replicas with higher throughput, modest energy consumption, and deterministic liveness guarantees. If complemented with heterogeneous trust and open membership, they have the potential to serve as blockchains backbone. This paper presents a general model of heterogeneous quorum systems where each participant can declare its own quorums, and captures the consistency, availability and inclusion properties of these systems. In order to support open membership, it then presents reconfiguration protocols for heterogeneous quorum systems including joining and leaving of a process, and adding and removing of a quorum, and further, proves their correctness in the face of Byzantine attacks. The design of the protocols is informed by the trade-offs that the paper proves for the properties that reconfigurations can preserve. The paper further presents a graph characterization of heterogeneous quorum systems, and its application for reconfiguration optimization. 

Local interactions of uncoordinated individuals produce the collective behaviors of many biological systems, inspiring much of the current research in programmable matter. A striking example is the spontaneous assembly of fire ants into "bridges" comprising their own bodies to traverse obstacles and reach sources of food. Experiments and simulations suggest that, remarkably, these ants always form one bridge - instead of multiple, competing bridges - despite a lack of central coordination. We argue that the reliable formation of a single bridge does not require sophistication on behalf of the individuals by provably reproducing this behavior in a self-organizing particle system. We show that the formation of a single bridge by the particles is a statistical inevitability of their preferences to move in a particular direction, such as toward a food source, and their preference for more neighbors. Two parameters, η and β, reflect the strengths of these preferences and determine the Gibbs stationary measure of the corresponding particle system’s Markov chain dynamics. We show that a single bridge almost certainly forms when η and β are sufficiently large. Our proof introduces an auxiliary Markov chain, called an "occupancy chain," that captures only the significant, global changes to the system. Through the occupancy chain, we abstract away information about the motion of individual particles, but we gain a more direct means of analyzing their collective behavior. Such abstractions provide a promising new direction for understanding many other systems of programmable matter. 

This paper studies the power of the "abstract MAC layer" model in a single-hop asynchronous network. The model captures primitive properties of modern wireless MAC protocols. In this model, Newport [PODC '14] proves that it is impossible to achieve deterministic consensus when nodes may crash. Subsequently, Newport and Robinson [DISC '18] present randomized consensus algorithms that terminate with O(n³ log n) expected broadcasts in a system of n nodes. We are not aware of any results on other fault-tolerant distributed tasks in this model. We first study the computability aspect of the abstract MAC layer. We present a wait-free algorithm that implements an atomic register. Furthermore, we show that in general, k-set consensus is impossible. Second, we aim to minimize storage complexity. Existing algorithms require Ω(n log n) bits. We propose two wait-free approximate consensus and two wait-free randomized binary consensus algorithms that only need constant storage complexity (except for the phase index). One randomized algorithm terminates with O(n log n) expected broadcasts. All our algorithms are anonymous, meaning that at the algorithm level, nodes do not need to have a unique identifier.