Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: A system and method to receive a query against a plurality of data objects that are sorted, at least conceptually, to follow a hierarchical order and support a preorder traversal arrangement and a postorder traversal arrangement; translate the query into an executable query plan including at least one instance of a hierarchy rearrange operator, the hierarchy rearrange operator to rearrange an input including one or more of the plurality of data objects from one of a preorder traversal arrangement and a postorder traversal arrangement to a corresponding opposite thereof; execute the executable query plan including the at least one instance of the hierarchy rearrange operator; and generate a query result based, at least in part, on the input of the one or more plurality of data objects being rearranged in the respective preorder traversal arrangement and a postorder traversal arrangement.

Abstract: A system includes determination, based on a plurality of rows of a table, where each of the plurality of rows associated with a respective row_id represents a respective a node of a hierarchy, row_id pairs of each parent node-child node pair of the hierarchy, execution, based on the row_id pairs, of a depth-first traversal of the hierarchy to sequentially add each row_id of the plurality of rows to a hierarchy index and receive a NODE value associated with the added row_id, and, for each of the plurality of rows, update of a row based on the NODE value associated with the row_id of the row.

Abstract: A system includes determination of a first interval encoding of a first version of a hierarchy of nodes, determination of a second version of the hierarchy of nodes, determination of a first difference between the first version of the hierarchy of nodes and the second version of the hierarchy of nodes, and determination of a first swap of two translation ranges of the first interval encoding, the first swap representing the first difference.

Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: A system includes storage of data of a hierarchy, where each node of the hierarchy is represented by a row, and each row includes a level of its respective node, a pointer to a lower bound entry of an order index structure associated with the hierarchy, and a pointer to an upper bound entry of the order index structure associated with the hierarchy, reception of a pointer l, and determination of an entry e of the order index structure to which the received pointer l points.

Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: A system includes a stored table comprising a plurality of rows and at least one column, each of the plurality of rows associated with a node of a hierarchy, and one of the at least one columns implicity representing a position of a row's associated node within the hierarchy, wherein a Structured Query Language query is received and, response to the query, one or more values of the one of the at least one columns are determined and one or more properties of the hierarchy are determined based on the one or more values.

Abstract: A system includes determination, based on a plurality of rows of a table, where each of the plurality of rows associated with a respective row_id represents a respective a node of a hierarchy, row_id pairs of each parent node-child node pair of the hierarchy, execution, based on the row_id pairs, of a depth-first traversal of the hierarchy to sequentially add each row_id of the plurality of rows to a hierarchy index and receive a NODE value associated with the added row_id, and, for each of the plurality of rows, update of a row based on the NODE value associated with the row_id of the row.

Abstract: A system and method to receive a query against a plurality of data objects that are sorted, at least conceptually, to follow a hierarchical order and support a preorder traversal arrangement and a postorder traversal arrangement; translate the query into an executable query plan including at least one instance of a hierarchy rearrange operator, the hierarchy rearrange operator to rearrange an input including one or more of the plurality of data objects from one of a preorder traversal arrangement and a postorder traversal arrangement to a corresponding opposite thereof; execute the executable query plan including the at least one instance of the hierarchy rearrange operator; and generate a query result based, at least in part, on the input of the one or more plurality of data objects being rearranged in the respective preorder traversal arrangement and a postorder traversal arrangement.

Abstract: A system includes determination, based on a plurality of rows of a table, where each of the plurality of rows associated with a respective row_id represents a respective a node of a hierarchy, row_id pairs of each parent node-child node pair of the hierarchy, execution, based on the row_id pairs, of a depth-first traversal of the hierarchy to sequentially add each row_id of the plurality of rows to a hierarchy index and receive a NODE value associated with the added row_id, and, for each of the plurality of rows, update of a row based on the NODE value associated with the row_id of the row.

Abstract: A system includes storage of data of a hierarchy, where each node of the hierarchy is represented by a row, and each row includes a level of its respective node, a pointer to a lower bound entry of an order index structure associated with the hierarchy, and a pointer to an upper bound entry of the order index structure associated with the hierarchy, reception of a pointer l, and determination of an entry e of the order index structure to which the received pointer l points.

Abstract: A system includes storage of data of a hierarchy, where each node of the hierarchy is represented by a row, and each row includes a level of its respective node, a pointer to a lower bound entry of an order index structure associated with the hierarchy, and a pointer to an upper bound entry of the order index structure associated with the hierarchy, reception of a pointer l, and determination of an entry e of the order index structure to which the received pointer l points.

Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: Addressed herein is the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Structural grouping is applied to relational algebra to provide concise syntax to express a class of useful computations. Algorithms are also provided to evaluate such structural groupings efficiently by exploiting available indexing schemes. Related apparatus, systems, techniques and articles are also described.

Abstract: A system includes generation of an encoding for each of a hierarchy of nodes, each of the nodes associated with one or more attributes, and the encoding for each node including a first pointer and a second pointer, and generation of an order tree comprising a hierarchy of entries, where each pointer of the encoding points to a respective one of the entries, wherein the encoding and the order tree indicate a position of each node in the hierarchy of nodes.

Abstract: A system includes storage of data of a hierarchy, where each node of the hierarchy is represented by a row, and each row includes a level of its respective node, a pointer to a lower bound entry of an order index structure associated with the hierarchy, and a pointer to an upper bound entry of the order index structure associated with the hierarchy, reception of a pointer l, and determination of an entry e of the order index structure to which the received pointer l points.