Related papers: The Maxflow problem and a generalization to simpli…

Clar number and Fries number are two thoroughly investigated parameters of plane graphs emerging from mathematical chemistry to measure stability of organic molecules. We consider first a common generalization of these two concepts for…

Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final…

While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…

Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows.…

We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.

We consider different online algorithms for a generalized scheduling problem for parallel machines, described in details in the first section. This problem is the generalization of the classical parallel machine scheduling problem, when the…

We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that…

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…

In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…

Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a…

We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…

The goal of this paper is to establish a decomposition of the network based on the maximum flow problem.

The proximal problem for structured penalties obtained via convex relaxations of submodular functions is known to be equivalent to minimizing separable convex functions over the corresponding submodular polyhedra. In this paper, we reveal a…

The vitality of an edge in a graph with respect to the maximum flow between two fixed vertices $s$ and $t$ is defined as the reduction of the maximum flow value caused by the removal of that edge. The max-flow vitality problem has already…

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…

This work consists of a study of a set of techniques and strategies related with algorithm's design, whose purpose is the resolution of problems on massive data sets, in an efficient way. This field is known as Algorithms for Big Data. In…

We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…

Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…

This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…