Uniquely-represented B-trees

A method, comprising:

• receiving, with one or more processors, data including one or more data elements;
• and
• constructing, with the one or more processors, a first level of a hierarchical data structure using the one or more data elements, wherein the hierarchical data structure is a B-tree including a plurality of different nodes arranged in a plurality of different levels, the constructing comprising:
• placing, with the one or more processors, the one or more data elements on the first level of the hierarchical data structure;
• computing, with the one or more processors, a result of a selection function applied to each one of the one or more data elements;
• moving, with the one or more processors, based on the result of the selection function for a given data element, the given data element to a second level of the hierarchical data structure;
• when more than one child data elements having a value less than the given data element remain in the first level of the hierarchical data structure, grouping, in a first grouped node, the child data elements;
• determining, with the one or more processors, based on the result of the selection function for an additional data element on the first level, whether the additional data element should be moved to the second level of the hierarchical data structure;
• wherein the hierarchical data structure has the same internal nodes and node representation regardless of the order of moving the given data element and the additional data element.

A system, comprising:

• one or more memories of a first computing device storing a first hierarchical data structure, wherein the first hierarchical data structure is a B-tree including a plurality of different nodes arranged in a plurality of different levels;
• one or more processors in communication with the one or more memories, the one or more processors configured to:
• receive first data to be committed in a distributed database, the first data including one or more data elements;
• compute a result of a selection function applied to each of the one or more data elements;
• identify, based on the result of the selection function for a first data element, a first node of the first hierarchical data structure;
• update the first node of the first hierarchical data structure using the first data element;
• identify, based on the result of the selection function for a second data element, a second node of the first hierarchical data structure maintained by the first computing device;
• updating, with one or more processors, the second node of the first hierarchical data structure using the second data element;
• wherein the first hierarchical data structure has the same internal nodes and node representation regardless of the order of updates of the first and second data elements.