相关论文: A Faster Algorithm for Quickest Transshipments via…
The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attention and played essential roles in many modern applications.…
Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves this problem…
The fast growing scale and heterogeneity of current communication networks necessitate the design of distributed cross-layer optimization algorithms. So far, the standard approach of distributed cross-layer design is based on dual…
This paper proposes an efficient HOT algorithm for solving the optimal transport (OT) problems with finite supports. We particularly focus on an efficient implementation of the HOT algorithm for the case where the supports are in…
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
We consider an off-line optimisation problem where $k$ robots must service $n$ requests on a single line. A request $i$ has weight $w_i$ and takes place at time $t_i$ at location $d_i$ on the line. A robot can service a request and collect…
Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative…
Computing exact Optimal Transport (OT) distances for large-scale datasets is computationally prohibitive. While entropy-regularized alternatives offer speed, they sacrifice precision and frequently suffer from numerical instability in…
In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization,…
In this paper, we study robust transshipment under consistent flow constraints. We consider demand uncertainty represented by a finite set of scenarios and characterize a subset of arcs as so-called fixed arcs. In each scenario, we require…
We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semi-discrete optimal transport problem with storage fees, corresponding to a problem with hard capacity constraints. This is a variant of the…
We provide universally-optimal distributed graph algorithms for $(1+\varepsilon)$-approximate shortest path problems including shortest-path-tree and transshipment. The universal optimality of our algorithms guarantees that, on any $n$-node…
Routing algorithms for public transport, particularly the widely used RAPTOR and its variants, often face performance bottlenecks during the transfer relaxation phase, especially on dense transfer graphs, when supporting unlimited…
The \Problem{knapsack} problem is a fundamental problem in combinatorial optimization. It has been studied extensively from theoretical as well as practical perspectives as it is one of the most well-known NP-hard problems. The goal is to…
Let $R$ and $B$ be two point sets in $\mathbb{R}^d$, with $|R|+ |B| = n$ and where $d$ is a constant. Next, let $\lambda : R \cup B \to \mathbb{N}$ such that $\sum_{r \in R } \lambda(r) = \sum_{b \in B} \lambda(b)$ be demand functions over…
Thresholding algorithms for sparse optimization problems involve two key components: search directions and thresholding strategies. In this paper, we use the compressed Newton direction as a search direction, derived by confining the…
Public transport administrators rely on efficient algorithms for various problems that arise in public transport networks. In particular, our study focused on designing linear-time algorithms for two fundamental path problems: the earliest…
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 present a pseudopolynomial-time algorithm for the Knapsack problem that has running time $\widetilde{O}(n + t\sqrt{p_{\max}})$, where $n$ is the number of items, $t$ is the knapsack capacity, and $p_{\max}$ is the maximum item profit.…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…