This paper deals with directed, bidirected, and undirected capacitated network design problems. Using mixed integer rounding (MIR), we generalize flow-cutset inequalities to these three link types and to an arbitrary modular link capacity structure, and propose a generic separation algorithm. In an extensive computational study on 54 instances from the Survivable Network Design Library (SNDlib)...

A graph G is chromatically k–connected if every vertex cutset induces a subgraph with chromatic number at least k. Thus, in particular each neighborhood has to induce a k–chromatic subgraph. In [3], Godsil, Nowakowski and Nešetřil asked whether there exists a k–chromatically connected graph such that every minimal cutset induces a subgraph with no triangles. We show that the answer is positive ...

This paper focuses on the capacity of point-to-point relay communications wherein the transmitter is assisted by an intermediate relay. We detail the mathematical model of cutset and amplify and forward (AF) relaying strategy. We present the upper bound capacity of each relaying strategy from information theory viewpoint and also in networks with Gaussian channels. We exemplify various outer re...

Let G be a finite graph with H as a star complement for a non-zero eigenvalue μ. Let κ′(G), δ(G) denote respectively the edge-connectivity and minimum degree of G. We show that κ′(G) is controlled by δ(G) and κ′(H). We describe the possibilities for a minimum cutset of G when μ 6∈ {−1, 0}. For such μ, we establish a relation between κ′(G) and the spectrum of H when G has a non-trivial minimum c...

Some problems related to security in communication networks lead to consider a new type of connectivity in graphs, namely the confidential connectivity. In this paper we present a characterization of unbreakable graphs using the notion of weak decomposition and we give some applications of minimal unbreakable graphs. In fact, we showed that a graph G is confidentially connected if and only if i...

1 Minimum Cuts In this lecture we will describe an algorithm that computes the minimum cut (or simply mincut) in an undirected graph. A c u t is deened as follows. by S is the subset of edges (ii j) 2 E such that jfii jg \ Sj = 1. That is, (S) consists of all those edges with exactly one endpoint in S. Given an undirected graph G = (V E) and for each edge e 2 E a nonnegative cost (or capacity) ...

In the Probabilistic Graphical Model (PGM) community there is an interest around tractable models, i.e., those that can guarantee exact inference even at the price of expressiveness. Structure learning algorithms are interesting tools to automatically infer both these architectures and their parameters from data. Even if the resulting models are efficient at inference time, learning them can be...

Given a network G = (V,E), we say that a subset of vertices S ⊆ V has radius r if it is spanned by a tree of depth r. We are interested in determining whether G has a cutset that can be written as the union of k sets of radius r. This generalizes the notion of k-vertex connectivity, since in the special case r = 0, a set spanned by a tree of depth r is a single vertex. Our motivation for consid...

This paper focuses on the capacity of peer-to-peer relay communications wherein the transmitter are assisted by an arbitrary number of parallel relays, i.e. there is no link and cooperation between the relays themselves. We detail the mathematical model of different relaying strategies including cutset and amplify and forward strategies. The cutset upper bound capacity is presented as a referen...