Related papers: The Maxflow problem and a generalization to simpli…
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…
We present a new strongly polynomial algorithm for generalized flow maximization that is significantly simpler and faster than the previous strongly polynomial algorithm [V\'egh16]. For the uncapacitated problem formulation, the complexity…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
Maxflow is a fundamental problem in graph theory and combinatorial optimisation, used to determine the maximum flow from a source node to a sink node in a flow network. It finds applications in diverse domains, including computer networks,…
The incorporation of region regularization into max-flow segmentation has traditionally focused on ordering and part-whole relationships. A side effect of the development of such models is that it constrained regularization only to those…
The minimum cost-flow problems have been attracted recently in optimization because of their applications in several areas of applied science and real life. Therefore, finding optima solution of these problems would be significant. Although…
The max-flow and max-coflow problem on directed graphs is studied in the common generalization to regular spaces, i.e., to kernels or row spaces of totally unimodular matrices. Exhibiting a submodular structure of the family of paths within…
I introduce a new approach to the maximum flow problem by a simple algorithm with a slightly better runtime. This approach is based on sorting arcs insight of vertices on a residual graph. This new approach leads to an O(mn^0.5) time bound…
We consider a nonlinear flow on simplicial complexes related to the simplicial Laplacian, and show that it is a generalization of various consensus and synchronization models commonly studied on networks. In particular, our model allows us…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
The Maximum Flow (Max-Flow) problem is a cornerstone in graph theory and combinatorial optimization, aiming to determine the largest possible flow from a designated source node to a sink node within a capacitated flow network. It has…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
Graphs are ubiquitous and ever-present data structures that have a wide range of applications involving social networks, knowledge bases and biological interactions. The evolution of a graph in such scenarios can yield important insights…
Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
Building on existing algorithms and results, we offer new insights and algorithms for various problems related to detecting maximal and maximum bicliques. Most of these results focus on graphs with small maximum degree, providing improved…