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We study the complexity of finding a subgraph of a certain size and a certain density, where density is measured by the average degree. Let γ : N → Q + be any density function, i.e., γ is computable in polynomial time and satisfies γ(k) ≤ k − 1 for all k ∈ N. Then γ-Cluster is the problem of deciding, given an undirected graph G and a natural number k,(More)
We contribute to the study of inferring commercial relationships between autonomous systems (AS relationships) from observable BGP routes. We deduce several forbidden patterns of AS relationships that impose a certain type of acyclicity on the AS graph. We investigate algorithms for solving the acyclic all-paths type-of-relationship problem, i.e., given a(More)
We consider a special kind of non-deterministic Turing machines. Cluster machines are distinguished by a neighbourhood relationship between accepting paths. Based on a for-malization using equivalence relations some subtle properties of these machines are proven. Moreover, by abstraction we gain the machine-independend concept of cluster sets which is the(More)
We introduce a general framework for the definition of function classes. Our model, which is based on polynomial time nondeterministic Turing transducers, allows uniform characterizations of FP, FPued classes (FewFP, NPMV) and many more. Each such class is defined in our model by a certain family of functions. We study a reducibility notion between such(More)
A complete classification of the computational complexity of the fixed-point existence problem for boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes F and graph classes G, an (F , G)-system is a boolean dynamical system such that all local transition functions lie in F and the(More)