Data imprecision under -geometry model: Range searching problem

Because of constraints in exact modeling, measuring and computing, it is inevitable thatalgorithms that solve real world problems have to avoid errors. hence, proposing models to handle error,and designing algorithms that work well in practice, are challenging fields. in this paper, we introduce amodel called the -geometry model to handle a dynamic form of imprecision, which allows the precision tochange monotonically in the input data of geometric algorithms. -geometry is a generalization of regionbasedmodels and provides the output of problems as functions, with respect to the level of precision.this type of output helps to design exact algorithms and is also useful in decision making processes.furthermore, we study the problem of orthogonal range searching in one and two dimensional spaceunder the model of -geometry, and propose efficient algorithms to solve it.