Related papers: Solving graph compression via optimal transport
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
Various graphs such as web or social networks may contain up to trillions of edges. Compressing such datasets can accelerate graph processing by reducing the amount of I/O accesses and the pressure on the memory subsystem. Yet, selecting a…
In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points source and destination, and it is not necessary to calculate the shortest path from source…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Logistics optimization nowadays is becoming one of the hottest areas in the AI community. In the past year, significant advancements in the domain were achieved by representing the problem in a form of graph. Another promising area of…
Graph neural networks can be effectively applied to find solutions for many real-world problems across widely diverse fields. The success of graph neural networks is linked to the message-passing mechanism on the graph, however, the…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
In 1966, Edward Nelson presented an interesting derivation of the Schrodinger equation using Brownian motion. Recently, this derivation is linked to the theory of optimal transport, which shows that the Schrodinger equation is a Hamiltonian…
Path optimization is a fundamental concern across various real-world scenarios, ranging from traffic congestion issues to efficient data routing over the internet. The Traffic Assignment Problem (TAP) is a classic continuous optimization…
This paper proposes a novel algorithm for signal classification problems. We consider a non-stationary random signal, where samples can be classified into several different classes, and samples in each class are identically independently…
In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy.…
In recent years studying the content of the World Wide Web became a very important yet rather difficult task. There is a need for a compression technique that would allow a web graph representation to be put into the memory while…
We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…