Related papers: GASP: A Gradient-Aware Shortest Path Algorithm for…
We propose a theoretical framework that generalizes simple and fast algorithms for hierarchical agglomerative clustering to weighted graphs with both attractive and repulsive interactions between the nodes. This framework defines GASP, a…
We have been interested in graphs and realizing them as Reeb graphs of explicit real algebraic functions. The Reeb graph of a differentiable function is the quotient space of the manifold of the domain, regarded as the space consisting of…
Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a…
The Reeb space, which generalizes the notion of a Reeb graph, is one of the few tools in topological data analysis and visualization suitable for the study of multivariate scientific datasets. First introduced by Edelsbrunner et al., it…
We give a new answer to so-called realization problems of graphs as Reeb graphs of smooth functions with prescribed preimages of regular values having nice structures. We present a best possible answer for functions on 3-dimensional closed…
Direct B-Rep generation is increasingly important in CAD workflows, eliminating costly modeling sequence data and supporting complex features. A key challenge is modeling joint distribution of the misaligned geometry and topology. Existing…
The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of level sets such that the set of all vertices coincides with the set of all connected components of level sets including…
The Reeb space is a fundamental data structure in computational topology that represents the fiber topology of a multi-field (or multiple scalar fields), extending the level set topology of a scalar field. Efficient algorithms have been…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
Graph data, essential in fields like knowledge representation and social networks, often involves large networks with many nodes and edges. Transmitting these graphs can be highly inefficient due to their size and redundancy for specific…
Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
In this work, we propose a graph-adaptive pruning (GAP) method for efficient inference of convolutional neural networks (CNNs). In this method, the network is viewed as a computational graph, in which the vertices denote the computation…
The Reeb graph is a construction that studies a topological space through the lens of a real valued function. It has widely been used in applications, however its use on real data means that it is desirable and increasingly necessary to…
Graph neural networks (GNNs) are prominent for their effectiveness in processing graph data for semi-supervised node classification tasks. Most works of GNNs assume that the observed structure accurately represents the underlying node…
Reeb graphs are structural descriptors that capture shape properties of a topological space from the perspective of a chosen function. In this work we define a combinatorial metric for Reeb graphs of orientable surfaces in terms of the cost…
The Reeb space of a function or a map on a manifold is defined as the space of all connected components of preimages and represents the manifold compactly. In fact, Reeb spaces are fundamental and useful tools in geometric theory of…
In this paper, we propose a new representation for multiview image sets. Our approach relies on graphs to describe geometry information in a compact and controllable way. The links of the graph connect pixels in different images and…
Reeb graphs are widely used in a range of fields for the purposes of analyzing and comparing complex spaces via a simpler combinatorial object. Further, they are closely related to extended persistence diagrams, which largely but not…
GraphBLAS is an interface for implementing graph algorithms. Algorithms implemented using the GraphBLAS interface are cast in terms of linear algebra-like operations. However, many graph algorithms are canonically described in terms of…