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Recursion represents an important addition to the SQL language. This work focuses on the optimization of linear recursive queries in SQL. To provide an abstract framework for discussion, we focus on computing the transitive closure of a graph. Three optimizations are studied: (1) Early evaluation of row selection conditions. (2) Eliminating duplicate rows in intermediate tables. (3) Defining an enhanced index to accelerate join computation. Optimizations are evaluated on two types of graphs: binary trees and sparse graphs. Binary trees represent an ideal graph with no cycles and a linear number of edges. Sparse graphs represent an average case with some cycles and a linear number of edges. In general, the proposed optimizations produce a significant reduction in the evaluation time of recursive queries.