Faster 3-Periodic Merging Networks

We consider the problem of merging two sorted sequences on a comparator network that is used repeatedly, that is, if the output is not sorted, the network is applied again using the output as input. The challenging task is to construct such networks of small depth. The first constructions of merging networks with a constant period were given by Kuty{\l}owski, Lory\'s and Oesterdikhoff. They have given $3$-periodic network that merges two sorted sequences of $N$ numbers in time $12\log N$ and a similar network of period $4$ that works in $5.67\log N$. We present a new family of such networks that are based on Canfield and Williamson periodic sorter. Our $3$-periodic merging networks work in time upper-bounded by $6\log N$. The construction can be easily generalized to larger constant periods with decreasing running time, for example, to $4$-periodic ones that work in time upper-bounded by $4\log N$. Moreover, to obtain the facts we have introduced a new proof technique

VOLUME ESTIMATION OF FUEL LOAD FOR HAZARD REDUCTION BURNING: A VOXEL APPROACH

The year 2020 started with more than 100 fires burning across Australia. Bushfire is a phenomenon that cannot be mitigated completely by human intervention; however, better management practices can help counter the increasing severity of fires. Hazard Reduction (HR) burning has become one of the resolute applications in the management of fire-prone ecosystems worldwide, where certain vegetation is deliberately burned under controlled circumstances to thin the fuel to reduce the severity of the bushfires. As the climate changes drastically, the severity of fires is predicted to increase in the coming years. Therefore, it becomes increasingly important to investigate automatic approaches to prevent, reduce and monitor the cause and movement of bushfires. Methods of assessing FL levels in Australia are commonly based on visual assessment guidelines, such as those described in the Overall Fuel Hazard Assessment Guide (OFHAG). The overall aim of this research is to investigate the use of LiDAR to estimate the volume of fuel load to assist in the planning of HR burning, an approach that could quantify the accumulation of elevated and near-surface FL with less time and cost. This research focuses on an innovative approach based on a voxel representation. A voxel is a volumetric pixel, a quantum unit of volume, and a numeric value of x, y and z to signify a value on a regular grid in a three-dimensional space. Voxels are beneficial for processing large pointcloud data and, specifically, computing volumes. Pointcloud data provides valuable three-dimensional information by capturing forest structural characteristics. The output of this research is to create a digitised map of the accumulation of fuel (vegetation) points at elevated fuel and near-surface fuel stratum based on the point density of the pointcloud dataset for Vermont Place Park, Newcastle, Australia. The output of this information is relayed through a digital map of fuel accumulation at elevated and near-surface fuel stratum. The result of this research provides a rough idea of where the highest amount of fuel is accumulated to assist in planning of an HR burn. This will help the fire practitioners/land managers determine at which location in the forest profile should be prioritised for HR burning. There is a short window to conduct HR burning that is why it is prevalent that a tool that can provide information on fuel at a fast pace could help the fire practitioner/land managers