Related papers: Tightening I/O Lower Bounds through the Hourglass …
This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…
A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed…
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…
Storage systems have not kept the same technology improvement rate as computing systems. As applications produce more and more data, I/O becomes the limiting factor for increasing application performance. I/O congestion caused by concurrent…
Large Language Models (LLMs) exhibit exceptional proficiency in handling extensive context windows in natural language. Nevertheless, the quadratic scaling of attention computation relative to sequence length creates substantial efficiency…
For many algorithmic problems, traditional algorithms that optimise on the number of instructions executed prove expensive on I/Os. Novel and very different design techniques, when applied to these problems, can produce algorithms that are…
Asymptotically tight lower bounds are derived for the I/O complexity of a general class of hybrid algorithms computing the product of $n \times n$ square matrices combining ``\emph{Strassen-like}'' fast matrix multiplication approach with…
We consider the ILP Feasibility problem: given an integer linear program $\{Ax = b, x\geq 0\}$, where $A$ is an integer matrix with $k$ rows and $\ell$ columns and $b$ is a vector of $k$ integers, we ask whether there exists…
We analyse some QR decomposition algorithms, and show that the I/O complexity of the tile based algorithm is asymptotically the same as that of matrix multiplication. This algorithm, we show, performs the best when the tile size is chosen…
In recent years a large number of problems have been considered in external memory models of computation, where the complexity measure is the number of blocks of data that are moved between slow external memory and fast internal memory…
Determining I/O lower bounds is a crucial step in obtaining communication-efficient parallel algorithms, both across the memory hierarchy and between processors. Current approaches either study specific algorithms individually, disallow…
We consider the problem of finding lower bounds on the I/O complexity of arbitrary computations in a two level memory hierarchy. Executions of complex computations can be formalized as an evaluation order over the underlying computation…
Many hierarchically modular systems are structured in a way that resembles an hourglass. This "hourglass effect" means that the system generates many outputs from many inputs through a relatively small number of intermediate modules that…
For most relevant computation, the energy and time needed for data movement dominates that for performing arithmetic operations on all computing systems today. Hence it is of critical importance to understand the minimal total data movement…
We present an I/O-efficient algorithm for computing similarity joins based on locality-sensitive hashing (LSH). In contrast to the filtering methods commonly suggested our method has provable sub-quadratic dependency on the data size.…
Online kernel selection is a fundamental problem of online kernel methods.In this paper,we study online kernel selection with memory constraint in which the memory of kernel selection and online prediction procedures is limited to a fixed…
We consider the well-known problem of enumerating all triangles of an undirected graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges, $M<E$ the size of internal memory, and…
We consider a broad class of first-order optimization algorithms which are \emph{oblivious}, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited side-information such as…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…