Related papers: Breaking the Quadratic Barrier: Robust Cardinality…

Cardinality estimation is a fundamental task in database management systems, aiming to predict query results accurately without executing the queries. However, existing techniques either achieve low estimation accuracy or incur high…

Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing…

This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\ldots,x_n$…

We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on $n$ vertices up to a $1+\epsilon$ error must…

Cardinality Estimation over Knowledge Graphs (KG) is crucial for query optimization, yet remains a challenging task due to the semi-structured nature and complex correlations of typical Knowledge Graphs. In this work, we propose GNCE, a…

Cost-based query optimization remains a critical task in relational databases even after decades of research and industrial development. Query optimizers rely on a large range of statistical synopses -- including attribute-level histograms…

Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits…

This paper develops conformal inference methods to construct a confidence interval for the frequency of a queried object in a very large discrete data set, based on a sketch with a lower memory footprint. This approach requires no knowledge…

Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…

Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…

This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…

In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic $k$-median and $k$-means problems, there…

Quantum computing platforms are evolving to a point where placing high numbers of qubits into a single core comes with certain difficulties such as fidelity, crosstalk, and high power consumption of dense classical electronics. Utilizing…

Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…

Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…

We study the problem of sketching an input graph, so that given the sketch, one can estimate the weight of any cut in the graph within factor $1+\epsilon$. We present lower and upper bounds on the size of a randomized sketch, focusing on…

Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and…

In this work, we present a dimensionality reduction algorithm, aka. sketching, for categorical datasets. Our proposed sketching algorithm Cabin constructs low-dimensional binary sketches from high-dimensional categorical vectors, and our…

One of the main problems in random network coding is to compute good lower and upper bounds on the achievable cardinality of the so-called subspace codes in the projective space $\mathcal{P}_q(n)$ for a given minimum distance. The…

Data sketches are approximate succinct summaries of long streams. They are widely used for processing massive amounts of data and answering statistical queries about it in real-time. Existing libraries producing sketches are very fast, but…