consideration of a plurality of logical expression representations of the original query and a plurality of alternative physical expression representations of the alternative logical expressions logical and physical expressions are represented as a directed acyclic graph dag of operators each table operator represents an operation that consumes one or more tables and produces a table each operator is evaluated in the context of the expression it is part of in order to determine the logical physical and estimated properties of the output table produced by the operator the properties of the output are typically a function of the properties of the input operators and the arguments to the operator a sql mr table operator can play the role of either a logical or physical operator during plan generation the process of evaluating the sql mr table operator properties involves performing a contract negotiation with the sql mr function instance the collaborative planning process allows the optimizer to exchange plan properties and context information about the surrounding query plan operators with a table operator as a result the optimizer can apply its rules and techniques to generate more optimal plans it also allows the author of the table operator to optimize its embedded logic the two novel aspects of the collaborative planning process are the following 1 the collaborative planning process determines and defines the plan and query properties to.