Enumeration of rooted partial subtrees

1. A method of executing instructions on at least one computing device including at least one processor and at least one memory, the method comprising:

executing the instructions on the at least one processor of the at least one computing device, wherein the instructions comprise instructions for database processing, and wherein the executing the instructions comprises:

representing stored content of a database, at least in part, as a data representation, wherein the data representation comprises a set of subtrees and/or partial subtrees;

representing a query as a numeral;

comparing the numeral with one or more numerals, wherein a result of the comparing is stored in the at least one memory of the at least one computing device;

enumerating the set of subtrees and/or partial subtrees for the data representation, or a portion thereof, wherein the set of subtrees and/or partial subtrees comprises at least a first partial subtree having a same node as a second partial subtree, and wherein the one or more numerals represent the set of subtrees and/or partial subtrees of the data representation as enumerated; and

returning at least one or more corresponding partial subtrees of the set of subtrees and/or partial subtrees based, at least in part, on the result of the comparing.

2. The method of claim 1 , wherein the data representation is a complex tree hierarchy.

3. The method of claim 1 , wherein the data representation is a multi-dimensional data representation.

4. The method of claim 1 , wherein the executing the instructions further comprises:

identifying one or more subtrees coupled to a root node of the data representation; and

enumerating a set of partial subtrees of the one or more subtrees that is identified.

5. The method of claim 4 , wherein the executing the instructions further comprises:

merging combinations of individual ones of the set of enumerated partial subtrees of the one or more subtrees that is identified.

6. The method of claim 5 , wherein the data representation is represented as a composite numeral, and wherein the identifying the one or more subtrees further comprises:

factoring the composite numeral.

7. The method of claim 1 , wherein the data representation comprises an edge labeled tree or a node labeled tree.

8. The method of claim 1 , wherein the at least one or more corresponding partial subtrees of the set of subtrees are returned in response to the query.

9. The method of claim 1 , wherein the data representation is represented, at least in part, via a hierarchical set of stored states, and wherein the partial subtrees represent at least a portion of the hierarchical set of stored states in the data representation.

10. The method of claim 1 , wherein the set of subtrees and/or partial subtrees of the data representation as enumerated comprises at least one of:

an empty tree; a single node tree; a tree comprising a subtree coupled to a root node of the data representation by an edge; or two or more trees coupled to a root node of the data representation by respective edges.

11. An apparatus comprising:

at least one computing device including at least one processor and at least one memory; and

the at least one memory to communicate instructions to the at least one processor and the at least one processor to execute the instructions communicated to the at least one processor, wherein the communicated instructions to be executed comprise instructions for database processing, and wherein the instructions for database processing to be executed comprise instructions to:

represent stored content of a database, at least in part, as a data representation, wherein the data representation to comprise a set of subtrees and/or partial subtrees;

represent a query as a numeral;

compare the numeral with one or more numerals, a result of the comparison being stored in the at least one memory of the at least one computing device;

enumerate the set of subtrees and/or partial subtrees for the data representation, or a portion thereof, wherein the set of subtrees and/or partial subtrees to comprise at least a first partial subtree to have a same node as a second partial subtree, and wherein the one or more numerals represent the set of subtrees and/or partial subtrees of the data representation as enumerated; and

return at least one or more corresponding partial subtrees of the set of subtrees and/or partial subtrees based, at least in part, on the result of the comparison.

12. The apparatus of claim 11 , wherein the instructions for database processing to be executed further comprise instructions to:

identify one or more subtrees to be coupled to a root node of the data representation; and

enumerate a set of partial subtrees of the one or more subtrees that is identified.

13. The apparatus of claim 12 , wherein the instructions for database processing to be executed further comprise instructions to:

merge combinations of individual ones of the set of enumerated partial subtrees of the one or more subtrees that is identified.

14. The apparatus of claim 13 , wherein the data representation is to be represented as a composite numeral, and wherein the instructions for database processing to be executed further comprise instructions to:

factor the composite numeral.

15. The apparatus of claim 11 , wherein the data representation is to be represented, at least in part, via a hierarchical set of stored states, and wherein the partial subtrees to represent at least a portion of a set of stored states in the data representation.

16. The apparatus of claim 11 , wherein the enumerated set of subtrees and/or partial subtrees of the data representation to comprise at least one of:

an empty tree; a single node tree; a tree that comprises a subtree to be coupled to a root node of the data representation by an edge; or two or more trees to be coupled to a root node of the data representation by respective edges.

17. An article comprising:

a non-transitory storage medium having machine-readable instructions stored thereon executable by at least one computing device comprising at least one processor and at least one memory, the at least one computing device to execute instructions on the at least one processor;

wherein the instructions to be executed to comprise instructions for database processing, and wherein the execution of the instructions for database processing comprises execution of instructions to:

represent stored content of a database, at least in part, as a data representation, wherein the data representation to comprise a set of subtrees and/or partial subtrees;

represent a query as a numeral;

compare the numeral with one or more numerals, a result of the comparison being stored in the at least one memory of the at least one computing device;

enumerate the set of subtrees and/or partial subtrees for the data representation, or a portion thereof, wherein the set of subtrees and/or partial subtrees to comprise at least a first partial subtree to have a same node as a second partial subtree, and wherein the one or more numerals represent the set of subtrees and/or partial subtrees of the data representation as enumerated; and

return at least one or more corresponding partial subtrees of the set of subtrees and/or partial subtrees based, at least in part, on the result of the comparison.

18. The article of claim 17 , wherein the non-transitory storage medium further comprises machine-readable instructions stored thereon to:

identify one or more subtrees to be coupled to a root node of the data representation; and

enumerate a set of partial subtrees of the one or more subtrees that is identified.

19. The article of claim 18 , wherein the non-transitory storage medium further comprises machine-readable instructions stored thereon to:

merge combinations of individual ones of the set of enumerated partial subtrees of the one or more subtrees that is identified.

20. The article of claim 19 , wherein the data representation is to be represented as a composite numeral, and wherein the non-transitory storage medium further comprises machine-readable instructions stored thereon to:

factor the composite numeral.