Related papers: Subquadratic Encodings for Point Configurations

For a static array A of n ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n+o(n) bits that allows to answer range minimum…

We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…

For many kinds of prefix-free codes there are efficient and compact alternatives to the traditional tree-based representation. Since these put the codes into canonical form, however, they can only be used when we can choose the order in…

One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…

Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…

In this work, we propose a new spatio-directional neural encoding that is compact and efficient, and supports all-frequency signals in both space and direction. Current learnable encodings focus on Cartesian orthonormal spaces, which have…

In the two-dimensional orthogonal colored range counting problem, we preprocess a set, $P$, of $n$ colored points on the plane, such that given an orthogonal query rectangle, the number of distinct colors of the points contained in this…

Let G be an embedded planar undirected graph that has n vertices, m edges, and f faces but has no self-loop or multiple edge. If G is triangulated, we can encode it using {4/3}m-1 bits, improving on the best previous bound of about 1.53m…

Let $S$ be a set of $n$ points in the plane. We present several different algorithms for finding a pair of points in $S$ such that any disk that contains that pair must contain at least $cn$ points of $S$, for some constant $c>0$. The first…

Object detection in point clouds is an important aspect of many robotics applications such as autonomous driving. In this paper we consider the problem of encoding a point cloud into a format appropriate for a downstream detection pipeline.…

The order-preserving model (op-model, in short) was introduced quite recently but has already attracted significant attention because of its applications in data analysis. We introduce several types of periods in this setting (op-periods).…

We consider planning problems on a punctured Euclidean spaces, $\mathbb{R}^D - \widetilde{\mathcal{O}}$, where $\widetilde{\mathcal{O}}$ is a collection of obstacles. Such spaces are of frequent occurrence as configuration spaces of robots,…

Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$\gamma$ (how well the given data are separated), the query complexity of the best-known…

In this paper, we develop new algorithms for the basic RNA folding problem. Given an RNA sequence that contains $n$ nucleotides, the goal of the problem is to compute a pseudoknot-free secondary structure that maximizes the number of base…

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…

Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of…

We present a number of new results about range searching for colored (or "categorical") data: 1. For a set of $n$ colored points in three dimensions, we describe randomized data structures with $O(n\mathop{\rm polylog}n)$ space that can…

We present the first optimal randomized algorithm for constructing the order-$k$ Voronoi diagram of $n$ points in two dimensions. The expected running time is $O(n\log n + nk)$, which improves the previous, two-decades-old result of Ramos…

Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a…

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…