Related papers: Succinct Data Structures for Retrieval and Approxi…
We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution…
An important function in modern routers and switches is to perform a lookup for a key. Hash-based methods, and in particular cuckoo hash tables, are popular for such lookup operations, but for large structures stored in off-chip memory,…
The computation of a peeling order in a randomly generated hypergraph is the most time-consuming step in a number of constructions, such as perfect hashing schemes, random $r$-SAT solvers, error-correcting codes, and approximate set…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and…
The performance of a dynamic dictionary is measured mainly by its update time, lookup time, and space consumption. In terms of update time and lookup time there are known constructions that guarantee constant-time operations in the worst…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
This paper proposes a framework for improving the operational efficiency of automated storage systems under uncertainty. It considers a 2D grid-based storage for uniform-sized loads (e.g., containers, pallets, or totes), which are moved by…
The tremendous expanse of search engines, dictionary and thesaurus storage, and other text mining applications, combined with the popularity of readily available scanning devices and optical character recognition tools, has necessitated…
We show that approximate similarity (near neighbour) search can be solved in high dimensions with performance matching state of the art (data independent) Locality Sensitive Hashing, but with a guarantee of no false negatives. Specifically,…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
In the total least squares problem, one is given an $m \times n$ matrix $A$, and an $m \times d$ matrix $B$, and one seeks to "correct" both $A$ and $B$, obtaining matrices $\hat{A}$ and $\hat{B}$, so that there exists an $X$ satisfying the…
Structural decomposition methods offer powerful theoretical guarantees for join evaluation, yet they are rarely used in real-world query optimizers. A major reason is the difficulty of combining cost-based plan search and structure-based…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map…
We consider the Low Rank Approximation problem, where the input consists of a matrix $A \in \mathbb{R}^{n_R \times n_C}$ and an integer $k$, and the goal is to find a matrix $B$ of rank at most $k$ that minimizes $\| A - B \|_0$, which is…
Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of…
There has been a recent trend in training neural networks to replace data structures that have been crafted by hand, with an aim for faster execution, better accuracy, or greater compression. In this setting, a neural data structure is…
We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path $\alpha$-minority queries. We present the first linear-space data structures, requiring $O(n…