A new continuous query to a data stream management system (DSMS) may use several operators that are equivalent to operators currently being used by continuous queries that have been previously registered in the DSMS. To determine equivalence of operators, the DSMS checks at least the function and the data input to the operators. On finding equivalence, the DSMS modifies a global plan being executed, to use at least an existing subtree of operators during execution of the new continuous query, to generate a modified plan. The DSMS is also programmed to cause each relation source operator (which outputs a relation) to propagate a current state of the relation to each operator newly coupled to the relational operator. After propagation of current state to newly-coupled operators, each operator in the modified plan processes any new data and supplies the result to all operators coupled thereto, including newly-coupled operators and existing operators.