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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)
In this paper, we study the problem of finding a periodic attractor of a Boolean network (BN), which arises in computational systems biology and is known to be NP-hard. Since a general case is quite hard to solve, we consider special but biologically important subclasses of BNs. For finding an attractor of period 2 of a BN consisting of n OR functions of(More)