相关论文: Unsplittable Euclidean Capacitated Vehicle Routing…

We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…

Let $S \subset \mathbb{R}^2$ be a set of $n$ sites. The unit disk graph $\text{UD}(S)$ on $S$ has vertex set $S$ and an edge between two distinct sites $s,t \in S$ if and only if $s$ and $t$ have Euclidean distance $|st| \leq 1$. A routing…

We develop a general framework for designing polynomial-time approximation schemes (PTASs) for various vehicle routing problems in trees. In these problems, the goal is to optimally route a fleet of vehicles, originating at a depot, to…

We study the problem of constructing $(1+\varepsilon)$-coresets for Euclidean $(k,z)$-clustering in the distributed setting, where $n$ data points are partitioned across $s$ sites. We focus on two prominent communication models: the…

Particle transport through an open, discrete 1-D channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by time dependent site energies, allows multiple occupation due to…

In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, and consequently, makes the air pollution enhance.…

We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…

We propose a combination of a bounding procedure and gradient descent method for solving the Dubins traveling salesman problem, that is, the problem of finding a shortest curvature-constrained tour through a finite number of points in the…

Given a set of points $P = (P^+ \sqcup P^-) \subset \mathbb{R}^d$ for some constant $d$ and a supply function $\mu:P\to \mathbb{R}$ such that $\mu(p) > 0~\forall p \in P^+$, $\mu(p) < 0~\forall p \in P^-$, and $\sum_{p\in P}{\mu(p)} = 0$,…

Among fundamental problems in the context of distributed computing by autonomous mobile entities, one of the most representative and well studied is {\sc Point Convergence}: given an arbitrary initial configuration of identical entities,…

This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…

Vehicle platooning facilitates the partial automation of vehicles and can significantly reduce fuel consumption. Mobile communication infrastructure makes it possible to dynamically coordinate the formation of platoons en route. We consider…

The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…

Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For $1$-parameter persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck…

We consider the capacitated clustering problem in general metric spaces where the goal is to identify $k$ clusters and minimize the sum of the radii of the clusters (we call this the Capacitated-$k$-sumRadii problem). We are interested in…

In the Time-Windows Unsplittable Flow on a Path problem (twUFP) we are given a resource whose available amount changes over a given time interval (modeled as the edge-capacities of a given path $G$) and a collection of tasks. Each task is…

We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on a class of grids in 2D and 3D Cartesian geometry that are regular at a coarse level but arbitrary within the coarse blocks. We describe these…

We propose a new speed and departure time optimization algorithm for the Pollution-Routing Problem (PRP), which runs in quadratic time and returns a certified optimal schedule. This algorithm is embedded into an iterated local search-based…

The min-max vehicle routing problem (min-max VRP) traverses all given customers by assigning several routes and aims to minimize the length of the longest route. Recently, reinforcement learning (RL)-based sequential planning methods have…

In this paper, we introduce a scalable model for the aggregate electricity demand of a fleet of electric vehicles, which can provide the right balance between model simplicity and accuracy. The model is based on classification of tasks with…