Related papers: New bounds for range closest-pair problems
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields…
In many real-world scenarios, multiple data providers need to collaboratively perform analysis of their private data. The challenges of these applications, especially at the big data scale, are time and resource efficiency as well as…
In plenty of machine learning applications, the most relevant items for a particular query should be efficiently extracted, while the relevance function is based on a highly-nonlinear model, e.g., DNNs or GBDTs. Due to the high…
The hitting set problem asks for a collection of sets over a universe $U$ to find a minimum subset of $U$ that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
Recent experiments suggest that certain data of $B \to \pi\pi,\pi K$ decays are inconsistent with the standard model expectations. We try to explain the discrepancies with R-parity violating suppersymmetry. By employing the QCD…
Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
Let $T$ be a tree space (or tree network) represented by a weighted tree with $t$ vertices, and $S$ be a set of $n$ stochastic points in $T$, each of which has a fixed location with an independent existence probability. We investigate two…
The bi-objective shortest-path (BOSP) problem seeks to find paths between start and target vertices of a graph while optimizing two conflicting objective functions. We consider the BOSP problem in the presence of correlated objectives. Such…
In the Stable Roommates Problem (SR), a set of $2n$ agents rank one another in a linear order. The goal is to find a matching that is stable: one that has no pair of agents who mutually prefer each other over their assigned partners. We…
Circle packing is widely used in visualization due to its aesthetic appeal and simplicity, particularly in tasks where the spatial arrangement and relationships between data are of interest, such as understanding proximity relationships…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed…
Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although it has been used with complex data, some adaptations were then necessary…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
The string indexing problem is a fundamental computational problem with numerous applications, including information retrieval and bioinformatics. It aims to efficiently solve the pattern matching problem: given a text T of length n for…
In a typical range emptiness searching (resp., reporting) problem, we are given a set $P$ of $n$ points in $\reals^d$, and wish to preprocess it into a data structure that supports efficient range emptiness (resp., reporting) queries, in…