Fachbereich Maschinenbau und Mechatronik
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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.
The rail business is challenged by long product life cycles and a broad spectrum of assembly groups and single parts. When spare part obsolescence occurs, quick solutions are needed. A reproduction of obsolete parts is often connected to long waiting times and minimum lot quantities that need to be purchased and stored. Spare part storage is therefore challenged by growing stocks, bound capital and issues of part ageing. A possible solution could be a virtual storage of spare parts which will be 3D printed through additive manufacturing technologies in case of sudden demand. As mechanical properties of additive manufactured parts are neither guaranteed by machine manufacturers nor by service providers, the utilization of this relatively young technology is impeded and research is required to address these issues. This paper presents an examination of mechanical properties of specimens manufactured from stainless steel through the selective laser melting (SLM) process. The specimens were produced in multiple batches. This paper interrogates the question if the test results follow a normal distribution pattern and if mechanical property predictions can be made. The results will be put opposite existing threshold values provided as the industrial standard. Furthermore, probability predictions will be made in order to examine the potential of the SLM process to maintain state-of-the-art mechanical property requirements.