Some mathematical properties of the performance measures applied for point cloud databases

Abstract. Data megatsunami remains a genuine challenge in a variety of scientific domains which typically focus on multidimensional objects. A distributed architecture is needed to store massive amounts of data. In such an environment, the optimization for data placement strategy is an important issue which has been of concern to researchers for several decades. To this purpose, tiling algorithms were presented in our previous work which can optimize data partitioning for load balancing and nearest neighbor search. These are based on a multidimensional histogram which can be utilized for data placement. Two performance measures were also introduced which can support the comparison of the efficiency of methods. This paper contributes by extending them with a new measure and examines the mathematical properties of these measures.