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Task offloading and scheduling in Mobile Edge Computing (MEC) are vital for meeting the low-latency demands of modern IoT and dynamic task scheduling scenarios. MEC reduces the processing burden on resource-constrained devices by enabling…
High-dimensional vector embeddings are widely used in retrieval systems, but they often suffer from noise, the curse of dimensionality, and slow runtime. However, dimensionality reduction (DR) is rarely applied due to its tendency to…
We present a new two-stage 3D object detection framework, named sparse-to-dense 3D Object Detector (STD). The first stage is a bottom-up proposal generation network that uses raw point cloud as input to generate accurate proposals by…
The Wasserstein distance is a discrepancy measure between probability distributions, defined by an optimal transport problem. It has been used for various tasks such as retrieving similar items in high-dimensional images or text data. In…
Point cloud segmentation (PCS) aims to separate points into different and meaningful groups. The task plays an important role in robotics because PCS enables robots to understand their physical environments directly. To process sparse and…
Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods,…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
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…
Recent 3D-based manipulation methods either directly predict the grasp pose using 3D neural networks, or solve the grasp pose using similar objects retrieved from shape databases. However, the former faces generalizability challenges when…
This paper presents the Cascaded Metric Tree (CMT) for efficient satisfaction of metric search queries over a dataset of N objects. It provides extra information that permits query algorithms to exploit all distance calculations performed…
A set of piecewise linear functions, called polylines, $P_1,\ldots,P_L$ each with at most $n$ vertices can be simplified into a polyline $M$ with $k$ vertices, such that the Fr\'echet distances $\epsilon_1,\ldots,\epsilon_L$ to each of…
We present a particle locating method for unstructured meshes in two and three dimensions. Our algorithm is based on a patch searching process, and includes two steps. We first locate the given point to a patch near a vertex, and then the…
Point clouds and meshes are widely used 3D data structures for many computer vision applications. While the meshes represent the surfaces of an object, point cloud represents sampled points from the surface which is also the output of…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
Current trends in the computer graphics community propose leveraging the massive parallel computational power of GPUs to accelerate physically based simulations. Collision detection and solving is a fundamental part of this process. It is…
We present a set of parallel algorithms for computing exact k-nearest neighbors in low dimensions. Many k-nearest neighbor algorithms use either a kd-tree or the Morton ordering of the point set; our algorithms combine these approaches…