Related papers: Impossibility Results for Grammar-Compressed Linea…
Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a-priori information about X is available at…
Given two positions $i$ and $j$ in a string $T$ of length $N$, a longest common extension (LCE) query asks for the length of the longest common prefix between suffixes beginning at $i$ and $j$. A compressed LCE data structure is a data…
We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size $n$, and when the input strings are run-length encoded and their compressed representations have size at most $m$.…
High-energy, large-scale particle colliders in nuclear and high-energy physics generate data at extraordinary rates, reaching up to $1$ terabyte and several petabytes per second, respectively. The development of real-time, high-throughput…
Training large language models (LLMs) is highly memory-intensive, as training must store not only weights and optimizer states but also intermediate activations for backpropagation. While existing memory-efficient methods largely focus on…
Linear-probing hash tables have been classically believed to support insertions in time $\Theta(x^2)$, where $1 - 1/x$ is the load factor of the hash table. Recent work by Bender, Kuszmaul, and Kuszmaul (FOCS'21), however, has added a new…
Repository-level code intelligence tasks require large language models (LLMs) to process long, multi-file contexts. Such inputs introduce three challenges: crucial context can be obscured by noise, truncated due to limited windows, and…
The recent advances in deep neural networks (DNNs) make them attractive for embedded systems. However, it can take a long time for DNNs to make an inference on resource-constrained computing devices. Model compression techniques can address…
Bitmap indexes are frequently used to index multidimensional data. They rely mostly on sequential input/output. Bitmaps can be compressed to reduce input/output costs and minimize CPU usage. The most efficient compression techniques are…
Graph neural networks (GNNs) are deep learning models designed specifically for graph data, and they typically rely on node features as the input to the first layer. When applying such a type of network on the graph without node features,…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
Working in the multitape Turing model, we show how to reduce the problem of matrix transposition to the problem of integer multiplication. If transposing an $n \times n$ binary matrix requires $\Omega(n^2 \log n)$ steps on a Turing machine,…
We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The…
We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
We present a new lossy compressor for discrete sources. For coding a source sequence $x^n$, the encoder starts by assigning a certain cost to each reconstruction sequence. It then finds the reconstruction that minimizes this cost and…
Packing and covering linear programs belong to the narrow class of linear programs that are efficiently solvable in parallel and distributed models of computation, yet are a powerful modeling tool for a wide range of fundamental problems in…
Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…