Related papers: A Flow Formulation for Horizontal Coordinate Assig…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant…
When the underlying physical network layer in optimal network flow problems is a large graph, the associated optimization problem has a large set of decision variables. In this paper, we discuss how the cycle basis from graph theory can be…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
This paper proposes a theoretical framework for modeling and optimizing the bounded functions based on the Fourier series approximation and Ricci flow. Specifically, the initial manifold, $\mathcal{M}_0$ is approximated using Fourier series…
In a directed graph $G$ with non-correlated edge lengths and costs, the \emph{network design problem with bounded distances} asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria…
A single-commodity congestion approximator for a graph is a compact data structure that approximately predicts the edge congestion required to route any set of single-commodity flow demands in a network. A hierarchical congestion…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…
This paper presents a novel control protocol for robust distance-based formation control with prescribed performance in which agents are subjected to unknown external disturbances. Connectivity maintenance and collision avoidance among…
We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…
This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
A popular way to plan trajectories in dynamic urban scenarios for Autonomous Vehicles is to rely on explicitly specified and hand crafted cost functions, coupled with random sampling in the trajectory space to find the minimum cost…
In this paper we present an O(n log n) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the arcs. If the source and the sink are on the same face, then…
This paper addresses the fuzzy shortest path problem in directed graphs, where edge costs are modeled as generalized fuzzy numbers with Gaussian membership functions. We interpret height as an indicator of information reliability. Based on…
This paper proposes a framework to guide an optical flow network with external cues to achieve superior accuracy either on known or unseen domains. Given the availability of sparse yet accurate optical flow hints from an external source,…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
This paper presents a general formulation to construct high order numerical schemes by using multi-moment constraint conditions on the flux function reconstruction. The new formulation, so called multi-moment constrained flux reconstruction…
We consider the problem of allocating a fixed amount of resource among nodes in a network when each node suffers a cost which is a convex function of the amount of resource allocated to it. We propose a new deterministic and distributed…
We present a global optimization approach to optical flow estimation. The approach optimizes a classical optical flow objective over the full space of mappings between discrete grids. No descriptor matching is used. The highly regular…