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With the continuous popularity of deep learning and representation learning, fast vector search becomes a vital task in various ranking/retrieval based applications, say recommendation, ads ranking and question answering. Neural network…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the…
This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
Consider the problem of partitioning an arbitrary metric space into pieces of diameter at most \Delta, such every pair of points is separated with relatively low probability. We propose a rate-based algorithm inspired by…
Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…
We propose two novel algorithms for constructing convex collision-free polytopes in robot configuration space. Finding these polytopes enables the application of stronger motion-planning frameworks such as trajectory optimization with…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
Aggregating different image features for image retrieval has recently shown its effectiveness. While highly effective, though, the question of how to uplift the impact of the best features for a specific query image persists as an open…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
We study algorithms and combinatorial complexity bounds for \emph{stable-matching Voronoi diagrams}, where a set, $S$, of $n$ point sites in the plane determines a stable matching between the points in $\mathbb{R}^2$ and the sites in $S$…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
A highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica and Matlab) do not offer a solution, is to find all the real solutions of a system of N nonlinear equations in a certain finite…
We present a theoretical and empirical analysis of the adaptive entry point selection for graph-based approximate nearest neighbor search (ANNS). We introduce novel concepts: $b\textit{-monotonic path}$ and $B\textit{-MSNET}$, which better…
Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we…
We consider the $(1+\varepsilon)$-Approximate Nearest Neighbour (ANN) Problem for polygonal curves in $d$-dimensional space under the Fr\'echet distance and ask to what extent known data structures for doubling spaces can be applied to this…
Early advancements in convolutional neural networks (CNNs) architectures are primarily driven by human expertise and by elaborate design processes. Recently, neural architecture search was proposed with the aim of automating the network…