Related papers: Reordering Columns for Smaller Indexes

Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the…

Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…

In some recent papers, researchers have found two very good methods for reordering columns within supernodes in sparse Cholesky factors; these reorderings can be very useful for certain factorization methods. The first of these reordering…

Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…

Scalable real-time assortment optimization has become essential in e-commerce operations due to the need for personalization and the availability of a large variety of items. While this can be done when there are simplistic assortment…

In many important applications -- such as search engines and relational database systems -- data is stored in the form of arrays of integers. Encoding and, most importantly, decoding of these arrays consumes considerable CPU time.…

Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering…

Compressed inverted indices in use today are based on the idea of gap compression: documents pointers are stored in increasing order, and the gaps between successive document pointers are stored using suitable codes which represent smaller…

In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…

We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…

The problem of column subset selection asks for a subset of columns from an input matrix such that the matrix can be reconstructed as accurately as possible within the span of the selected columns. A natural extension is to consider a…

Neural document ranking approaches, specifically transformer models, have achieved impressive gains in ranking performance. However, query processing using such over-parameterized models is both resource and time intensive. In this paper,…

It is commonly accepted in the practice of on-line analytical processing of databases that the multidimensional database organization is less scalable than the relational one. It is easy to see that the size of the multidimensional…

Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…

Sorting and binary searching a dense array can be considered the simplest and most space efficient form of indexing. This holds especially on GPUs as they exhibit exceptional sorting performance. However, the popular opinion is that such a…

As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…

We present a fast multiscale approach for the network minimum logarithmic arrangement problem. This type of arrangement plays an important role in a network compression and fast node/link access operations. The algorithm is of linear…

Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…

Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how to convert a compression…

Moving data through the memory hierarchy is a fundamental bottleneck that can limit the performance of core algorithms of machine learning, such as convolutional neural networks (CNNs). Loop-level optimization, including loop tiling and…