Summary: The W3C SPARQL working group is defining the new SPARQL 1.1 query language. The current working draft of SPARQL 1.1 focuses mainly on the description of the language. In this paper, we provide a formalization of the syntax and semantics of the SPARQL 1.1 federation extension, an important fragment of the language that has not yet received much attention. Besides, we propose optimization techniques for this fragment, provide an implementation of the fragment including these techniques, and carry out a series of experiments that show that our optimization procedures significantly speed up the query evaluation process.