Simulation of Join Cardinalities in Random Databases Using Poisson Stochastic Processes

Abstract: In this paper, using Poisson stochastic processes, we introduce an approach to the problem of the approximate join operation in random databases. It is shown that the cardinalities of the result sets obtained from an approximate join operation follow this type of stochastic process. Initially, we treat the case of the approximate join between two random tables, which is accomplished using a homogeneous bidimensional Poisson process. Further, we extend the obtained result to the case of the multiple join. This generalization is made through a multidimensional Poisson process. As a consequence, the algorithms that simulate these processes can also simulate the cardinalities of the sets resulting from the approximate join operation