Query processing remains one of the important challenges of Object-Oriented Database Management Systems. Query optimization involves creating alternative executing plans for a given query and executing the least costly one.

The object-oriented database management systems store references to objects (precomputed joins), and use path expressions in query languages and there is no previous work describing the selectivities and costs of path expressions. However it is clear that to be able to optimize the object-oriented query languages involving path expressions, it is essential to calculate their costs and selectivities. This information is necessary for deciding whether to use pointer chasing or to convert the path expressions into explicit joins and also for deciding the execution order of path expressions. In this paper, we provide the formulas for the costs of forward and backward path traversals.