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Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let h_min(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal binary search tree with near minimal height, i.e.\ with height h <= h_min(n) + Delta for some fixed Delta. It is shown, that for any fixed Delta optimal binary search trees with near minimal height can be constructed in time O(n^2). This is as fast as in the unrestricted case. So far, the best known algorithms for the construction of height-restricted optimal binary search trees have running time O(L n^2), whereby L is the maximal permitted height. Compared to these algorithms our algorithm is at least faster by a factor of log n, because L is lower bounded by log n.
The development of robot control programs is a complex task. Many robots are different in their electrical and mechanical structure which is also reflected in the software. Specific robot software environments support the program development, but are mainly text-based and usually applied by experts in the field with profound knowledge of the target robot. This paper presents a graphical programming environment which aims to ease the development of robot control programs. In contrast to existing graphical robot programming environments, our approach focuses on the composition of parallel action sequences. The developed environment allows to schedule independent robot actions on parallel execution lines and provides mechanism to avoid side-effects of parallel actions. The developed environment is platform-independent and based on the model-driven paradigm. The feasibility of our approach is shown by the application of the sequencer to a simulated service robot and a robot for educational purpose.