Fachbereich Maschinenbau und Mechatronik
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Is part of the Bibliography
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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.
Entwicklung eines Kletterroboters zur Diagnose und Instandsetzung von Windenergieanlagen (SMART)
(2016)
The production and assembly of customized products increases the demand for flexible automation systems. One approach is to remove the safety fences that separate human and industrial robot to combine their skills. This collaboration possesses a certain risk for the human co-worker, leading to numerous safety concepts to protect him. The human needs to be monitored and tracked by a safety system using different sensors. The proposed system consists of a RGBD camera for surveillance of the common working area, an array of optical distance sensors to compensate shadowing effects of the RGBD camera and a laser range finder to detect the co-worker when approaching the work cell. The software for collision detection, path planning, robot control and predicting the behaviour of the co-worker is based on the Robot Operating System (ROS). A first prototype of the work cell shows that with advanced algorithms from the field of mobile robotics a very flexible safety concept can be realized: the robot not simply stops its movement when detecting a collision, but plans and executes an alternative path around the obstacle.
We prove characterizations of the existence of perfect ƒ-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the ƒ-factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the ƒ-factor problem is NP-hard.