Related papers: Parallelism and Time in Hierarchical Self-Assembly
We consider the classical scheduling problem on parallel identical machines to minimize the makespan, and achieve the following results under the Exponential Time Hypothesis (ETH) 1. The scheduling problem on a constant number $m$ of…
The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set…
Assembling genomic sequences from a set of overlapping reads is one of the most fundamental problems in computational biology. Algorithms addressing the assembly problem fall into two broad categories -- based on the data structures which…
Optimization techniques for decreasing the time and area of adder circuits have been extensively studied for years mostly in binary logic system. In this paper, we provide the necessary equations required to design a full adder in…
In this paper, we propose and investigate a novel memory architecture for neural networks called Hierarchical Attentive Memory (HAM). It is based on a binary tree with leaves corresponding to memory cells. This allows HAM to perform memory…
Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…
Self-assembly in the laboratory can now yield `information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires…
We study asynchronous finite sum minimization in a distributed-data setting with a central parameter server. While asynchrony is well understood in parallel settings where the data is accessible by all machines -- e.g., modifications of…
Replication time is among the most important components of a bacterial cell's reproductive fitness. Paradoxically, larger cells replicate in less time than smaller cells despite the fact that building a larger cell requires increased…
Hierarchically structured natural materials possess functionalities unattainable to the same components organized or mixed in simpler ways. For instance, the bones and teeth of mammals are far stronger and more durable than the mineral…
We examine a computational geometric problem concerning the structure of polymers. We model a polymer as a polygonal chain in three dimensions. Each edge splits the polymer into two subchains, and a dihedral rotation rotates one of these…
A large number of NP-hard graph problems can be solved in $f(w)n^{O(1)}$ time and space when the input graph is provided together with a tree decomposition of width $w$, in many cases with a modest exponential dependence $f(w)$ on $w$.…
General matrix multiplication (GEMM) is the computational backbone of modern AI workloads, and its efficiency is critically dependent on effective tiling strategies. Conventional approaches employ symmetric tile buffering, where the…
The modular design of planar phased arrays arranged on orthogonal polygon-shaped apertures is addressed and a new method is proposed to synthesize domino-tiled arrays fitting multiple, generally conflicting, requirements. Starting from an…
We show that the number of distinct squares in a packed string of length $n$ over an alphabet of size $\sigma$ can be computed in $O(n/\log_\sigma n)$ time in the word-RAM model. This paper is the first to introduce a sublinear-time…
We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by…
Given a set $Z$ of $n$ positive integers and a target value $t$, the Subset Sum problem asks whether any subset of $Z$ sums to $t$. A textbook pseudopolynomial time algorithm by Bellman from 1957 solves Subset Sum in time $O(nt)$. This has…
Self-assembly is a fundamental concept in biology and of significant interest to nanotechnology. Significant progress has been made in characterizing and controlling the properties of the resulting structures, both experimentally and…
A key principle in string processing is local consistency: using short contexts to handle matching fragments of a string consistently. String synchronizing sets [Kempa, Kociumaka; STOC 2019] are an influential instantiation of this…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…