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An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus on enumerative algorithms for the computation of the equitable coloring number and propose a general scheme to derive pruning rules for them: We show how the extendability of a partial coloring into an equitable coloring can be modeled via network flows. Thus, we obtain pruning rules which can be checked via flow algorithms. Computational experiments show that the search tree of enumerative algorithms can be significantly reduced in size by these rules and, in most instances, such naive approach even yields a faster algorithm. Moreover, the stability, i.e., the number of solved instances within a given time limit, is greatly improved.
Since the execution of flow algorithms at each node of a search tree is time consuming, we derive arithmetic pruning rules (generalized Hall-conditions) from the network model. Adding these rules to an enumerative algorithm yields an even larger runtime improvement.
Since fluid-structure interaction within the finite-element method is state of the art in many engineering fields, this method is used in voice analysis. A quasi two-dimensional model of the vocal folds including the ventricular folds is presented. First results of self-sustained vocal fold oscillation are presented and possibilities as well as limitations are discussed.
A Formulation of Quantum Stochastic Processes and Some of its Properties. Hellwig, K.-E.; Stulpe, W.
(1983)
IT Products are viewed and managed differently depending on the perspectives and the stage within the life cycle. A model is presented that integrates different perspectives and stages serving as an aid for the analysis of business models and focused positioning of IT-products. Four generic business models are analysed with regard to the product management function in general and the positioning field for IT-products specifically: off-the-shelf (license), license plus service, project, and system service (incl. cloud computing).