A cost function for uniformly partitioned UB-trees

Most of the operations of the relational algebra or of SQL (such as projection with duplicate elimination, joins, ordering, group-by and aggregations) are efficiently processed using a sorted stream of tuples. Often, these operations are combined with restrictions in one or several attributes. Previous research has proposed algorithms for efficiently dealing with this kind of query pattern, which is highly relevant with respect to data warehousing, data mining and GIS (geographic information systems). In this paper, we present a cost model that enables a concise estimation of both memory costs and run-time costs for processing queries with restrictions in multiple attributes that may in addition involve a sort operation. Our cost model considers uniformly distributed UB-trees (universal B-trees) with independent dimensions, and it is derived analytically in three steps, starting with a very simple, perfectly idealized partitioning scheme, moving on to imperfect partitioning schemes, and finally evaluating a probabilistically partitioned UB-tree. We also reason to what extent our cost model might be taken into account if the data is not distributed uniformly, by investigating the connection between the cost model and selectivities.