Related papers: The Maxflow problem and a generalization to simpli…
We consider approximation algorithms for the problem of finding $x$ of minimal norm $\|x\|$ satisfying a linear system $\mathbf{A} x = \mathbf{b}$, where the norm $\|\cdot \|$ is arbitrary and generally non-Euclidean. We show a simple…
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under…
Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
We consider a generalized Ricci flow with a given (not necessarily closed) three-form and establish the higher derivatives estimates for compact manifolds. As an application, we prove the compactness theorem for this generalized Ricci flow.…
We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows,…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
In a certain sense a perfect fluid is a generalization of a point particle. This leads to the question as to what is the corresponding generalization for extended objects. The lagrangian formulation of a perfect fluid is much generalized…
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
The simplification of a multigraph into a simple graph can be abstracted to a more general comma category under some common conditions. When using the identity functor, the category of simple objects in a comma category generalizes the…
We study the robust maximum flow problem and the robust maximum flow over time problem where a given number of arcs $\Gamma$ may fail or may be delayed. Two prominent models have been introduced for these problems: either one assigns flow…
This work aims to make it easier for a specialist in one field to find and explore ideas from another field which may be useful in solving a new problem arising in his practice. It presents a methodology which serves to represent the…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
This paper describes work carried out on a model for the evolution of graph classes in complex objects. By defining evolution rules and propagation strategies on graph classes, we aim to define a user-definable means to manage data…
In 2010s Fleiner introduced a notion of stable flows in directed networks and showed that such a flow always exists and can be found by use of a reduction to the stable allocation problem due to Baiou and Balinski. Recently Cseh and…