Related papers: Parallelism and Time in Hierarchical Self-Assembly
We investigate pseudo-polynomial time algorithms for Subset Sum. Given a multi-set $X$ of $n$ positive integers and a target $t$, Subset Sum asks whether some subset of $X$ sums to $t$. Bringmann proposes an $\tilde{O}(n + t)$-time…
We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…
We consider the selection problem on a completely connected network of $n$ processors with no shared memory. Each processor initially holds a given numeric item of $b$ bits allowed to send a message of $\max ( b, \lg n )$ bits to another…
Given a multiset $S$ of $n$ positive integers and a target integer $t$, the Subset Sum problem asks to determine whether there exists a subset of $S$ that sums up to $t$. The current best deterministic algorithm, by Koiliaris and Xu…
3D printing enables the fabrication of complex architectures by automating long sequences of additive steps. The increasing sophistication of printers, materials, and generative design promises to make geometric complexity a non-issue in…
This paper proposes a scalable planning algorithm for creating defect-free atom arrays in neutral-atom systems. The algorithm generates a $\mathcal{O}(\sqrt N)$ time plan for $N$ atoms by parallelizing atom transport using a two-dimensional…
Cycles are one of the fundamental subgraph patterns and being able to enumerate them in graphs enables important applications in a wide variety of fields, including finance, biology, chemistry, and network science. However, to enable cycle…
The rapid rise in demand for training large neural network architectures has brought into focus the need for partitioning strategies, for example by using data, model, or pipeline parallelism. Implementing these methods is increasingly…
In this paper we consider the problem of scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of…
We present a self-stabilizing algorithm for the (asynchronous) unison problem which achieves an efficient trade-off between time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
Fast algorithms for the computation of $N$-body problems can be broadly classified into mesh-based interpolation methods, and hierarchical or multiresolution methods. To this last class belongs the well-known fast multipole method (FMM),…
In this work, we present a novel class of parallelizable high-order time integration schemes for the approximate solution of additive ODEs. The methods achieve high order through a combination of a suitable quadrature formula involving…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind…
Squares (fragments of the form $xx$, for some string $x$) are arguably the most natural type of repetition in strings. The basic algorithmic question concerning squares is to check if a given string of length $n$ is square-free, that is,…
We consider the problem of augmenting an $n$-vertex tree with one shortcut in order to minimize the diameter of the resulting graph. The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of…
Microstructural geometry plays a critical role in the response of heterogeneous materials. Consequently, methods for generating microstructural samples are increasingly crucial to advanced numerical analyses. We extend Sonon et al.'s…
We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle $C_n$, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of $n \geq 3$, and runs in…
Width parameterizations of SAT, such as tree-width and path-width, enable the study of computationally more tractable and practical SAT instances. We give two simple algorithms. One that runs simultaneously in time-space…