Related papers: Fast Witness Counting
The gist of many (NP-)hard combinatorial problems is to decide whether a universe of $n$ elements contains a witness consisting of $k$ elements that match some prescribed pattern. For some of these problems there are known advanced…
Many combinatorial problems involve determining whether a universe of $n$ elements contains a witness consisting of $k$ elements which have some specified property. In this paper we investigate the relationship between the decision and…
In this paper, we introduce a general framework for fine-grained reductions of approximate counting problems to their decision versions. (Thus we use an oracle that decides whether any witness exists to multiplicatively approximate the…
We use lookup tables to design faster algorithms for important algebraic problems over finite fields. These faster algorithms, which only use arithmetic operations and lookup table operations, may help to explain the difficulty of…
Given two vectors $u,v \in \mathbb{Q}^D$ over a finite domain $D$ and a function $f : D\times D\to D$, the convolution problem asks to compute the vector $w \in \mathbb{Q}^D$ whose entries are defined by $w(d) = \sum_{\substack{x,y \in D \\…
In recent years much effort was put into developing polynomial-time conditional lower bounds for algorithms and data structures in both static and dynamic settings. Along these lines we suggest a framework for proving conditional lower…
Visual object counting is a fundamental computer vision task underpinning numerous real-world applications, from cell counting in biomedicine to traffic and wildlife monitoring. However, existing methods struggle to handle the challenge of…
An important question that arises in the study of high dimensional vector representations learned from data is: given a set $\mathcal{D}$ of vectors and a query $q$, estimate the number of points within a specified distance threshold of…
For a set $S$ of $n$ disjoint line segments in $\mathbb{R}^{2}$, the visibility counting problem is to preprocess $S$ such that the number of visible segments in $S$ from any query point $p$ can be computed quickly. There have been…
Consider the following parameterized counting variation of the classic subset sum problem, which arises notably in the context of higher homotopy groups of topological spaces: Let $\mathbf{v} \in \mathbb{Q}^d$ be a rational vector, $(T_{1},…
Learning to count is a learning strategy that has been recently proposed in the literature for dealing with problems where estimating the number of object instances in a scene is the final objective. In this framework, the task of learning…
Visual object counting is a fundamental computer vision task in industrial inspection, where accurate, high-throughput inventory tracking and quality assurance are critical. Moreover, manufactured parts are often too light to reliably…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
Counting the number of items in a visual scene remains a fundamental yet challenging task in computer vision. Traditional approaches to solving this problem rely on domain-specific counting architectures, which are trained using datasets…
Detecting and counting copies of permutation patterns are fundamental algorithmic problems, with applications in the analysis of rankings, nonparametric statistics, and property testing tasks such as independence and quasirandomness…
We present a zero-crossings counting problem that is a generalization of the Bernstein-Vazirani problem. The goal of this problem is to count the number of zero-crossings (or sign changes) in a special type of sequence S, whose definition…
Sketching has emerged as a powerful technique for speeding up problems in numerical linear algebra, such as regression. In the overconstrained regression problem, one is given an $n \times d$ matrix $A$, with $n \gg d$, as well as an $n…
The Closest Vector Problem (CVP) is a computational problem in lattices that is central to modern cryptography. The study of its fine-grained complexity has gained momentum in the last few years, partly due to the upcoming deployment of…
The celebrated Morris counter uses $\log_2\log_2 n + O(\log_2 \sigma^{-1})$ bits to count up to $n$ with a relative error $\sigma$, where if $\hat{\lambda}$ is the estimate of the current count $\lambda$, then…
We study the problems of counting the homomorphisms, counting the copies, and counting the induced copies of a $k$-vertex graph $H$ in a $d$-degenerate $n$-vertex graph $G$. Our main result establishes exhaustive and explicit complexity…