Given two point sets A and B in ℝ d of size n each, for some constant dimension d≥ 1, and a
parameter ε> 0, we present a deterministic algorithm that computes, in n·(ε− 1 log n) O (d) …

We study vertex sparsification for distances, in the setting of planar graphs with distortion:
Given a planar graph G (with edge weights) and a subset of k terminal vertices, the goal is to …

Due to their flexibility and agility, unmanned aerial vehicles (UAVs) offer a promising
approach to cluster planning within wireless sensor networks (WSNs). However, the limited …

Algorithms for the minimum-cost bipartite matching can be used to estimate Wasserstein
distance between two distributions. Given two sets $ A $ and $ B $ of $ n $ points in a $2 …

We consider the problem of computing the 1-Wasserstein distance W (µ, ν) between two d-
dimensional discrete distributions µ and ν whose support lie within the unit hypercube …

Optimal Transport (OT, also known as the Wasserstein distance) is a popular metric for
comparing probability distributions and has been successfully used in many machine …

Many real-world problems can be formulated as the alignment between two geometric
patterns. Previously, a great amount of research focus on the alignment of two-dimensional …

For two point sets A, B⊂ Rd, with| A|=| B|= n and d> 1 a constant, and for a parameter ε> 0,
we present a randomized algorithm that, with probability at least 1/2, computes in O (n (ε− O …

The Earth Mover's Distance is a popular similarity measure in several branches of computer
science. It measures the minimum total edge length of a perfect matching between two point …

Given a set of points P=\left(P^+⊔P^-\right)⊂R^d for some constant d and a supply function
μ:P→R such that μ(p)\gt 0∀p∈P^+,μ(p)\lt0∀p∈P^-, and p∈Pμ(p)=0, the geometric …