Abstract: Described are systems and methods relating to database query optimization and query cost estimation. The approach is described in the context of searching balanced and semi-balanced tree indexes such as B-trees, B+ trees, and R-B trees. The described approach may be used for both simple and composite queries, and the described approach may be used for relational queries, i.e., where a variable is less than or greater than a certain value and the database is being used to find the set of records that satisfy the relation. Further, the described approach may be used for generalized N-ary tree queries and cost estimations.