arXiv subjects

Garrett Parzych

Publications and source records attributed to Garrett Parzych.

3 recordsLinked to original sources

arXiv2026

Adaptive Self-Organization in Anonymous Dynamic Networks

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 closely approximate $r(s)$, a goal distribution defined by the problem instance. By symmetry, deterministic nodes can only hope to solve homogeneous instances of adaptive self-organization, i.e., those in which all nodes stabilize with the same color. We present a linear-time, logarithmic-memory, deterministic algorithm for this class of instances that works even when the multiplicity and location of signal witnesses change arbitrarily. We then give a randomized extension of this algorithm that solves arbitrary (i.e., not necessarily homogeneous) instances of adaptive self-organization with high probability in the same time and space bounds.

cs.DC↗

arXiv2025

Open, Reproducible Calculation of Assembly Indices

We present assembly-theory, a Rust package for computing assembly indices of covalently bonded molecular structures. This is a key complexity measure of assembly theory, a recent theoretical framework quantifying selection across diverse systems, most importantly chemistry. assembly-theory is designed for researchers and practitioners alike, providing (i) extensible, high-performance implementations of assembly index calculation algorithms, (ii) comprehensive benchmarks against which current and future algorithmic improvements can be tested, and (iii) Python bindings and RDKit-compatible data loaders to support integration with existing computational pipelines.

physics.chem-ph↗

arXiv2024

Memory Lower Bounds and Impossibility Results for Anonymous Dynamic Broadcast

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 $\Omega(\log n)$ 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 $\omega(1)$ 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.

cs.DC↗