No abstract

The complexity of randomized incremental algorithms is analyzed with the assumption of a random order of the input. To guarantee this hypothesis, the n data have to be known in advance in order to be mixed what contradicts with the on-line nature of the algorithm. We present the shuffling buffer technique to introduce sufficient randomness to guarantee an improvement on the worst case complexity by knowing only k data in advance. Typically, an algorithm with O(n2) worst-case complexity and O(n) or O(n log n) randomized complexity has an [Formula: see text] complexity for the shuffling buffer. We illustrate this with binary search trees, the number of Delaunay triangles or the number of trapezoids in a trapezoidal map created during an incremental construction.

Assessing the solid wood content is crucial when acquiring stacked roundwood. A frequently used method for this is to multiply determined conversion factors by the measured gross volume. However, the conversion factors are influenced by several log and stack parameters. Although these parameters have been identified and studied, their individual influence has not yet been analyzed using a broad statistical basis. This is due to the considerable financial resources that the data collection entails. To overcome this shortcoming, a 3D-simulation model was developed. It generates virtual wood stacks of randomized composition based on one individual data set of logs, which may be real or defined by the user. In this study, the development and evaluation of the simulation model are presented. The model was evaluated by conducting a sensitivity and a quantitative analysis of the simulation outcomes based on real measurements of 405 logs of Norway spruce and 20 stacks constituted with these. The results of the simulation outcomes revealed a small overestimation of the net volume of real stacks: by 1.2% for net volume over bark and by 3.2% for net volume under bark. Furthermore, according to the calculated mean bias error (MBE), the model underestimates the gross volume by 0.02%. In addition, the results of the sensitivity analysis confirmed the capability of the model to adequately consider variations in the input parameters and to provide reliable outcomes.

Robustness problems due to the substitution of the exact computation on real numbers by the rounded floating point arithmetic are often an obstacle to obtain practical implementation of geometric algorithms. If the adoption of the exact computation paradigm [C.K. Yap, T. Dubé, The exact computation paradigm, in: D.] gives a satisfactory solution to this kind of problems for purely combinatorial algorithms, this solution does not allow to solve in practice the case of algorithms that cascade the construction of new geometric objects. In this report, we consider the problem of rounding the intersection of two polygonal regions onto the integer lattice with inclusion properties. Namely, given two polygonal regions A and B having their vertices on the integer lattice, the inner and outer rounding modes construct two polygonal regions A ∩ B and A ∩ B with integer vertices such that A ∩ B ⊆ A ∩ B ⊆ A ∩ B. We also prove interesting results on the Hausdorff distance, the size and the convexity of these polygonal regions.

Robustness problems due to the substitution of the exact computation on real numbers by the rounded floating point arithmetic are often an obstacle to obtain practical implementation of geometric algorithms. If the adoption of the exact computation paradigm [13] gives a satisfactory solution to this kind of problems for purely combinatorial algorithms, this solution does not allow to solve in practice the case of algorithms that cascade the construction of new geometric objects. In this paper, we consider the problem of rounding the intersection of two polygonal regions onto the integer lattice with inclusion properties. Namely, given two polygonal regions A and B having their vertices on the integer lattice, the inner and outer rounding modes construct two polygonal regions A ∩ B and A ∩ B with integer vertices suchWe also prove interesting results on the Hausdorff distance, the size and the convexity of these polygonal regions.