Related papers: Analysis of Farthest Point Sampling for Approximat…
Sampling is an essential part of raw point cloud data processing such as in the popular PointNet++ scheme. Farthest Point Sampling (FPS), which iteratively samples the farthest point and performs distance updating, is one of the most…
In this paper we introduce Farthest Sampling Segmentation (FSS), a new method for segmentation of triangulated surfaces, which consists of two fundamental steps: the computation of a submatrix $W^k$ of the affinity matrix $W$ and the…
Computing shortest path distances between nodes lies at the heart of many graph algorithms and applications. Traditional exact methods such as breadth-first-search (BFS) do not scale up to contemporary, rapidly evolving today's massive…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…
Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few…
Processing large point clouds is a challenging task. Therefore, the data is often sampled to a size that can be processed more easily. The question is how to sample the data? A popular sampling technique is Farthest Point Sampling (FPS).…
The Traveling Salesman Problem (TSP) is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
For regression tasks one often leverages large datasets for training predictive machine learning models. However, using large datasets may not be feasible due to computational limitations or high data labelling costs. Therefore, suitably…
Point-based Neural Networks (PNNs) have become a key approach for point cloud processing. However, a core operation in these models, Farthest Point Sampling (FPS), often introduces significant inference latency, especially for large-scale…
Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…
Geodesic distance, sometimes called shortest path length, has proven useful in a great variety of applications, such as information retrieval on networks including treelike networked models. Here, our goal is to analytically determine the…
Point cloud analytics has become a critical workload for embedded and mobile platforms across various applications. Farthest point sampling (FPS) is a fundamental and widely used kernel in point cloud processing. However, the heavy external…
Machine learning model development in chemistry and materials science often grapples with the challenge of small scale, unbalanced labelled datasets, a common limitation in scientific experiments. These dataset imbalances can precipitate…
Given a simple polygon $P$ and a set $Q$ of points contained in $P$, we consider the geodesic $k$-center problem where we want to find $k$ points, called \emph{centers}, in $P$ to minimize the maximum geodesic distance of any point of $Q$…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
In the $k$-Cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. Prior work on this problem gives, for all $h…
We discuss two versions of the Fr\'echet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance…
We consider a random graph G(n,p) whose vertex set V has been randomly embedded in the unit square and whose edges are given weight equal to the geometric distance between their end vertices. Then each pair {u,v} of vertices have a distance…
The Euclidean $k$-means problem is a classical problem that has been extensively studied in the theoretical computer science, machine learning and the computational geometry communities. In this problem, we are given a set of $n$ points in…