相关论文: Large-scale semi-discrete optimal transport with d…

We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

To date, location privacy protection is a critical issue in Location-Based Services (LBS). In this work, we propose a novel geometric framework based on the classical discrete geometric structure, the Voronoi-Delaunay duality (VDD). We…

Let $P$ be a set of $n$ points and $Q$ a convex $k$-gon in ${\mathbb R}^2$. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of $P$, under the convex distance…

We leverage powerful mathematical tools stemming from optimal transport theory and transform them into an efficient algorithm to reconstruct the fluctuations of the primordial density field, built on solving the Monge-Amp\`ere-Kantorovich…

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…

We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method…

We develop a new approach for distributed distance computation in planar graphs that is based on a variant of the metric compression problem recently introduced by Abboud et al. [SODA'18]. One of our key technical contributions is in…

This note discusses an essentially decentralized interior point method, which is well suited for optimization problems arising in energy networks. Advantages of the proposed method are guaranteed and fast local convergence also for problems…

We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This…

We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises…

We introduce a novel property of bounded Voronoi tessellations that enables cycle-free mesh sweeping algorithms. We prove that a topological sort of the dual graph of any Voronoi tessellation is feasible in any flow direction and dimension,…

Although deep neural networks are well-known for their outstanding performance in tackling complex tasks, their hunger for computational resources remains a significant hurdle, posing energy-consumption issues and restricting their…

We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…

We propose a GPU-based distributed optimization algorithm, aimed at controlling optimal power flow in multi-phase and unbalanced distribution systems. Typically, conventional distributed optimization algorithms employed in such scenarios…

Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…

This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered…

Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets…

This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…