Related papers: Efficient Algorithms for Cardinality Estimation an…
The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine learning and statistics, and the design of…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
Modern database optimizer relies on cardinality estimator, whose accuracy directly affects the optimizer's ability to choose an optimal execution plan. Recent work on data-driven methods has leveraged probabilistic models to achieve higher…
Over finite fields, if the image of a polynomial map is not the entire field, then its cardinality can be bounded above by a significantly smaller value. Earlier results bound the cardinality of the value set using the degree of the…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
Cardinality estimation (CardEst), a central component of the query optimizer, plays a significant role in generating high-quality query plans in DBMS. The CardEst problem has been extensively studied in the last several decades, using both…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse…
We develop general methods to obtain fast (polynomial time) estimates of the cardinality of a combinatorially defined set via solving some randomly generated optimization problems on the set. Geometrically, we estimate the cardinality of a…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
Maximizing a monotone submodular function under cardinality constraint $k$ is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction,…
Border bases can be considered to be the natural extension of Gr\"obner bases that have several advantages. Unfortunately, to date the classical border basis algorithm relies on (degree-compatible) term orderings and implicitly on reduced…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
Query optimizers rely on accurate cardinality estimation (CardEst) to produce good execution plans. The core problem of CardEst is how to model the rich joint distribution of attributes in an accurate and compact manner. Despite decades of…
A long-standing open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs…
Estimating the output size of a query is a fundamental yet longstanding problem in database query processing. Traditional cardinality estimators used by database systems can routinely underestimate the true output size by orders of…
We present precise bit and degree estimates for the optimal value of the polynomial optimization problem $f^*:=\text{inf}_{x\in \mathscr{X}}~f(x)$, where $\mathscr{X}$ is a semi-algebraic set satisfying some non-degeneracy conditions. Our…
Cardinality estimation has long been grounded in statistical tools for density estimation. To capture the rich multivariate distributions of relational tables, we propose the use of a new type of high-capacity statistical model: deep…
Cardinality estimation is a fundamental task in database systems and plays a critical role in query optimization. Despite significant advances in learning-based cardinality estimation methods, most existing approaches remain difficult to…