In some recently proposed extensions to relational database systems as well as in deductive databases a database system is presented with a collection of just one it is an interesting problem then, to come up with algorithms that process these queries together instead of one query at a time we examine the problem of multiple (global) query optimization in this paper a hierarchy of algorithms that can be used for global query optimization is exhibited and analyzed these algorithms range from an arbitrary serial execution without any sharing of common results among the queries to an exhaustive search of all possible ways to process all queries.