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This article proposes a linear integer programming formulation and several heuristics based on GRASP and path relinking for the antibandwidth problem. In the antibandwidth problem, one is given an undirected graph with n nodes and must label the nodes in a way that each node receives a unique label from the set {1, 2,…,n}, such that, among all adjacent node pairs, the minimum difference between the...
The R‐MAT graph generator introduced by Chakrabarti et al (Int Conf Data Mining, 2004) offers a simple, fast method for generating very large directed graphs. These properties have made it a popular choice as a method of generating graphs for objects of study in a variety of disciplines, from social network analysis to high performance computing. We analyze the graphs generated by R‐MAT and model...
We discuss 11 known basic models of distributed computing: four message‐passing models that differ by the (non)existence of port‐numbers and a hierarchy of seven local computations models. In each of these models, we study the computational complexity of the decision problems if the leader election and if the naming problem can be solved on a given network. It is already known that these two decision...
A graph is said to be edge‐superconnected if each minimum edge‐cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a
$\{d,d+1\}$‐semiregular graph if all its vertices have degree either d or $d+1$. A smallest $\{d,d+1\}$‐semiregular graph G with girth g is said to be a $(\{d,d+1\};g)$‐cage. We show that every $(\{d,d+1\};g)$‐cage with odd girth g is...
In an inverse network absolute (or vertex) 1 ‐center location problem the parameters of a given network, like edge lengths or vertex weights, have to be modified at minimum total cost such that a prespecified vertex s becomes an absolute (or a vertex) 1 ‐center of the network. In this article, the inverse absolute and vertex 1 ‐center location problems on unweighted trees with n + 1 vertices are considered...
The connected hub number hc(G) of a connected graph G is the smallest order of a connected subgraph H of G such that any two nonadjacent vertices of G − H are joined in G by a path with all internal vertices in H. Letting γc(G) denote the connected domination number of G, it is easy to see that hc(G) ≤ γc(G) ≤ hc(G) + 1 for every connected graph G. Here we characterize the graphs G for which γc(G)...
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