Three-dimensional probabilistic data structure

1. A method, comprising;

maintaining, by a database node, a data structure used to encode a plurality of database keys, wherein the data structure includes a plurality of levels, each of which includes a character-addressable matrix that encodes transitions between characters;

inserting, by the database node, a database key into the data structure, wherein the database key comprises a series of characters with a plurality of transitions between two successive characters, wherein the inserting includes encoding the plurality of transitions across the plurality of levels such that different ones of the plurality of transitions are encoded in different ones of the plurality of levels, and wherein a given transition is encoded by setting, in a character-addressable matrix that corresponds to the given transition, an indication at a matrix location addressed using the two successive characters of the given transition; and

maintaining, in association with the indication by the database node, lineage information that specifies a set of database key lineages, a given one of which specifies one or more characters of a particular inserted database key that precede the two successive characters that are also in that particular inserted database key.

2. The method of claim 1 , wherein the lineage information is stored separately from the plurality of levels that include the indication, and wherein the indication is a pointer that identifies a location where the lineage information is stored.

3. The method of claim 1 , wherein each database key lineage maintained in association with the data structure identifies a same number of characters.

4. The method of claim 1 , wherein the indication, for the two successive characters, corresponds to at least two different database keys that have been inserted into the data structure.

5. The method of claim 4 , wherein the set of database key lineages includes a respective database key lineage for each of the at least two different database keys.

6. The method of claim 1 , further comprising:

sending, by the database node to a second database node, the data structure to enable the second database node to determine whether to request a database record from the database node; and

receiving, by the database node from the second database node, a second data structure that enables the database node to determine whether to request a database record from the second database node.

7. The method of claim 6 , further comprising:

determining, by the database node, whether to request a database record for a particular database key, wherein the determining includes:

determining whether the second data structure includes levels that store indications that are indicative of transitions between successive characters included in the particular database key; and

in response to determining that the second data structure includes levels storing indications that are indicative of the transitions between successive characters included in the particular database key, the database node sending a request to the second database node for a database record associated with the particular database key.

8. The method of claim 7 , wherein the determining whether to request a database record further includes:

calculating a plurality of database key lineages that correspond to the transitions between successive characters included in the particular database key; and

comparing the plurality of database key lineages against database key lineages maintained in association with the indications.

9. The method of claim 1 , wherein the inserting includes:

storing, in a corresponding level of the plurality of levels, an indication that is indicative of a transition from a last character of the series of characters to a terminal character separate from the series of characters.

10. A non-transitory computer readable medium having program instructions stored thereon that are capable of causing a computer system to perform operations comprising:

writing a database record to a particular location;

inserting a database key associated with the database record into a data structure, wherein the database key comprises a series of characters with a plurality of transitions between two successive characters, wherein the data structure includes a plurality of levels, each of which includes a character-addressable matrix that is capable of encoding one of the plurality of transitions, and wherein the inserting includes:

encoding the plurality of transitions across the plurality of levels such that different ones of the plurality of transitions are encoded in different ones of the plurality of levels, wherein a given transition is encoded by setting, in the character-addressable matrix that corresponds to the given transition, an indication at a matrix location addressed using the two successive characters of the given transition;

maintaining lineage information in association with the indication, wherein the lineage information specifies a set of database key lineages, a given one of which specifies one or more characters of a particular inserted database key that precede the two successive characters that are also in that particular inserted database key; and

sending, to another computer system, the data structure to enable the other computer system to determine whether to request a database record from the particular location.

11. The non-transitory computer readable medium of claim 10 , wherein the indication identifies the lineage information.

12. The non-transitory computer readable medium of claim 10 , wherein the operations further comprise:

prior to inserting the database key into the data structure, allocating the data structure such that a particular character-addressable matrix in the plurality of levels has a particular memory size;

prior to sending the data structure to the other computer system, performing a compression operation on the data structure, wherein the compression operation includes:

determining that a memory size of data written to the particular character-addressable matrix does not consume a threshold amount of the particular memory size; and

replacing the particular character-addressable matrix with particular data in another format, wherein the particular data is indicative of the data written to the particular character-addressable matrix.

13. The non-transitory computer readable medium of claim 10 , wherein the operations further comprise:

in response to inserting a threshold number of database keys into the data structure, creating a second data structure in which to insert subsequent database keys.