The fifth generation (5G) system architecture is defined as service-based and the core network functions are described as sets of services accessible through application programming interfaces (API). One of the components of 5G is Multi-access Edge Computing (MEC) which provides the open access to radio network functions through API. Using the mobile edge API third party analytics applications ...

A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G − X must have at least two vertices. The restricted connectivity κ′(G) of a connected graph G is defined as the minimum cardinality of a restricted cut. Additionally, if the deletion of a minimum restricted cut isolates on...

In this paper, the concept of hypergraph is extended to the fuzzy hypergraph. In the fuzzy hypergraph, the concepts of a-cut hypergraph, strength of edge and dual fuzzy hypergraph are developed. It is shown that the fuzzy hypergraph and a-cut hypergraph are useful to represent a fuzzy partition. An application example also shows that the strength of edge can be used to decompose the data set in...

Motivated by an application in network security, we investigate the following “linear” case of Directed Multicut. Let G be a directed graph which includes some distinguished vertices t1, . . . , tk. What is the size of the smallest edge cut which eliminates all paths from ti to tj for all i < j? We show that this problem is fixed-parameter tractable when parametrized in the cutset size p via an...

Introduction to graphs, Paths, cycles and trails Max-flow min-cut theorem, computing max s-t flows and min-cut Edge and Vertex Connectivity and Menger's theorem Maximum matching, Hall's theorem, algorithms for computing maximum matching in weighted and unweighted graphs. Edge and vertex colouring of graphs. Independent sets Planar graphs and algorithms for checking for planarity. The course nee...

An elegant and general way to apply graph partitioning algorithms to hypergraphs would be to model hypergraphs by graphs and apply the graph algorithms to these models Of course such models have to simulate the given hypergraphs with respect to their cut properties An edge weighted graph V E is a cut model for an edge weighted hypergraph V H if the weight of the edges cut by any bipartition of ...