8. A processor-implemented method to execute on one or more processors that perform the method, comprising: receiving an original query plan comprising query nodes that include one or more database operations; transforming the original query plan into an equivalent executable compact query plan comprising at least two source nodes including scan operations to source tables, the at least two source nodes coupled to at least one abstract node and at least one singleton node, wherein a child of the at least one abstract node comprises at least one of the source nodes or the at least one singleton node, but not another abstract node, wherein the at least one singleton node comprises a single operation selected from aggregate, union, order by, or null accepting full outer join, wherein the at least one abstract node comprises a set of operations selected from at least one of Cartesian product, evaluation, filter, left outer join, or null rejecting full outer join, and wherein the at least one abstract node is partitioned into multiple intra-partition commutable operations that can be executed in a different order from the original query plan based on upward compatibility or a combination of a single null rejecting left outer join operation and the multiple intra-partition commutable operations; and storing the compact query plan on a machine readable device.
8. A processor-implemented method to execute on one or more processors that perform the method, comprising: receiving an original query plan comprising query nodes that include one or more database operations; transforming the original query plan into an equivalent executable compact query plan comprising at least two source nodes including scan operations to source tables, the at least two source nodes coupled to at least one abstract node and at least one singleton node, wherein a child of the at least one abstract node comprises at least one of the source nodes or the at least one singleton node, but not another abstract node, wherein the at least one singleton node comprises a single operation selected from aggregate, union, order by, or null accepting full outer join, wherein the at least one abstract node comprises a set of operations selected from at least one of Cartesian product, evaluation, filter, left outer join, or null rejecting full outer join, and wherein the at least one abstract node is partitioned into multiple intra-partition commutable operations that can be executed in a different order from the original query plan based on upward compatibility or a combination of a single null rejecting left outer join operation and the multiple intra-partition commutable operations; and storing the compact query plan on a machine readable device. 12. The method of claim 8 , further comprising: traversing the query nodes of the original query plan; and forming additional abstract nodes in the compact query plan when a Cartesian product (C) operator, Filter (F) operator, Evaluation (E) operator, a Left Outer Join (LOJ) operator, or null-rejecting Full Outer Join (FOJ rej ) operator is encountered in the original query plan.