In the rectilinear Steiner arborescence problem the task is to build a shortest rectilinear Steiner tree connecting a given root and a set of terminals which are placed in the plane such that all root-terminal-paths are shortest paths. This problem is known to be NP-hard. In this paper we consider a more restricted version of this problem. In our case we have a depth restrictions d(t) ∈ N for e...

A configuration of the Abelian sandpile model is called recurrent if grains of sand can be added to it so that the resulting configuration relaxes to the original one; else it is called transient. Given a transient configuration, a recurrent configuration results after adding enough grains of sand. In the case of a three-dimensional sandpile model, it is shown in this paper that the problem of ...

The appearance of the theory of zero-knowledge, presented by Goldwasser, Micali and Rackoff in 1985, opened a way to secure identification schemes. The first application was the famous Fiat-Shamir scheme based on the problem of modular square roots extraction. In the following years, many other schemes have been proposed, some Fiat-Shamir extensions but also new discrete logarithm based schemes...

The use of ontologies and ontology mappings is increasing in companies. Often the same context is modeled in different ontologies. Mapping is necessary to integrate these ontologies; however, in many cases these mappings are incorrect, i.e., they incorrectly link semantic concepts with different meanings. Tools that validate these mappings are necessary to ensure reliable communication between ...

We consider the ~ATISFIABILITY problem (~-SAT): Given a family F of n clauses cl, ._, , c, in conjunctive normal form, each consisting of k literals corresponding to k different variables of a set of r 2 k 2 1 boolean variables, is F satisfiable? By k-SAT@ no) we denote the k-SAT problem restricted to families with n > n,(r) clauses. We prove that for each k > 3 and each integer I > 4 such that...

We consider the family of graph problems called node-deletion problems, defined as follows: For a fixed graph property l7, what is the minimum number of nodes which must be deleted from a given graph so that the resulting subgraph satisfies l7? We show that if l7 is nontrivial and hereditary on induced subgraphs, then the node-deletion problem for n is NP-complete for both undirected and direct...

The classical degree sequence problems for simple graphs are computationally easy. In the last years numerous new construction problems were introduced (for example the joint degree matrix problems and its variants) which are still easy. Network scientists would like to generate networks with more and more constraints and it is expected that the complexity of constructing networks with prescrib...

There exists a method using Ordered Binary Decision Diagrams (OBDDs) to solve combinatorial problems. In the method, Boolean variables are de ned and a Boolean function is constructed as an OBDD whose value is 1 for assignments which satisfy conditions of a problem. In this paper, we improve the method. As the values of almost all variables are xed before the construction of the OBDD, our algor...

We show that the edge disjoint paths problem is NP-complete in directed or undirected rectangular grids, even if the union G + H of the supply and the demand graph is Eulerian.