BytesTrie

This is an idea for a trie that is intended to be fairly simple but also fairly efficient and versatile. It maps from arbitrary byte sequences to 32-bit integers. (Small non-negative integers are stored more efficiently. Negative integers are the least efficient.)

Input strings would be mapped to byte sequences. Invariant-character strings could be used directly, if the trie was built for the appropriate charset family, or we could map EBCDIC input to ASCII (while lowercasing for case-insensitive matching).

For Thai DBBI, each of U+0E00..U+0EFF could be mapped to its low byte.

For CJK DBBI, we could use UTF-16BE or a slight variant of it. For general Unicode strings (e.g., time zone names), we could devise a simple encoding that maps printable ASCII to single bytes, Unihan & Hangul and some other ranges to two bytes per character, and the rest to three bytes per character. (We could also use this for CJK DBBI, to reduce the number of such "converters".) Or, we use a UCharsTrie for those.

Sample code is attached.

See the UCharsTrie sibling page for some more details. The BytesTrie and UCharsTrie structures are nearly the same, except that the UCharsTrie uses fewer, larger units.

See also the diagram of a BytesTrie for a sample set of string-to-value mappings.

Design points

• • The BytesTrie and UCharsTrie are designed to be byte-serialized/UChar-serialized, for trivial platform swapping.

  • Compact: Small values and jump deltas should be encoded in few bytes. This requires variable-length encodings.

  • The length of each value/delta is encoded either in a preceding node or in its own lead unit. This makes skipping values efficient, and fewer units need to be range-checked while reading variable-length values.

  • Nodes with small values are encoded in single units.

  • Linear-match nodes match a sequence of units without choice/selection.

  • Branches

    • Branches store relative deltas to "jump" to following nodes. Small deltas are encoded in single units; encoding deltas is much more efficient than encoding absolute offsets.

    • Variable-width values make binary search on branch nodes infeasible. Therefore, branches with lists of (key, value) pairs are limited to short list lengths for linear search.

    • For large branches, branch nodes contain one unit, for branching to the left (less-than) or to the right (greater-or-equal). This encodes a binary search into the data structure.

      • Initially, I had an equals edge in split-branch sub-nodes as well, but that slowed down matching significantly (9% in one case) without noticeably helping with the serialized size (0.2% in that case).

    • At the end of each node (except for a final-value node), matching continues with the next node, rather than using another jump to a different location.

    • Each branch head node encodes the length of the branch (the number of units to select from). The split-branch and list-branch sub-nodes do not have node heads. Instead, the code tracks the remaining length of the branch, halving it for each split-branch edge and counting down in a list-branch sub-node.

    • The maximum length of a list-branch sub-node is fixed, that is, part of the serialized data format and cannot be changed compatibly. This constant is used in the branching code to decide whether to split less-than/greater-or-equal vs. walk a list of key-value pairs.

    • This constant must be at least 3 so that split-branch sub-nodes have a length of at least 4 so that the following list-branch nodes have a length of at least 2 and can use a do-while loop rather than a while loop. (Saving one length check.)

    • I explored an alternative, with only split-branch nodes down to length 1 and then a final match unit with continuing matching after that. It was fast but also significantly larger. A branch like this is about twice the size of a key-value pair list. If the average list-branch length is n, a branch has (length/n)-1 split-branch sub-nodes. This experiment corresponds to n=1.

  • API

    • The API is simple and low-level. At the core, next(unit) "turns the crank" and returns basically a 2-bit result that encodes matches() (this unit continues a matching sequence), hasNext() (another unit can continue a matching sequence) and hasValue() (the units so far are a matching string).

    • Higher-level functions that handle different input (e.g., normalize units on the fly) and provide variations of functionality (e.g., longest match, startsWith, find all matches from some point in text, ...) can be built on top of the low-level functions without cluttering the API or pulling in further dependencies.

    • The next(unit) function stops on a value node rather than decoding the value, saving time until the value is requested (via getValue()). The following next(unit2) call will then skip over the value node.

    • There is enough API to serve a variety of uses, including matching/mapping whole strings, finding out if a prefix belongs only to strings with the same value, getting all units that can continue from some point, and getting all (string, value) pairs. This should be able to support lookups, parsing with abbreviations, word segmentation, etc.

  • The "fast" builder code is simple. The builder builds, it need not use a trie structure until writing the serialized form, and it need not provide any of the trie runtime API.

  • There is builder code that makes a "small" trie, attempting to avoid writing duplicate nodes. This is possible when whole trees of nodes are the same and at least one is reached via a "jump" delta which can "jump" to the previously written serialization of such a tree.