# Radix trees in R

#### Oliver Keyes

#### 2023-03-04

A radix tree, or trie, is a data structure optimised for storing key-value pairs in a way optimised for searching. This makes them very, very good for efficiently matching data against keys, and retrieving the values associated with those keys.

`triebeard` provides an implementation of tries for R (and one that can be used in Rcpp development, too, if that’s your thing) so that useRs can take advantage of the fast, efficient and user-friendly matching that they allow.

## Radix usage

Suppose we have observations in a dataset that are labelled, with a 2-3 letter code that identifies the facility the sample came from:

    labels <- c("AO-1002", "AEO-1004", "AAI-1009", "AFT-1403", "QZ-9065", "QZ-1021", "RF-0901",
                "AO-1099", "AFT-1101", "QZ-4933")

We know the facility each code maps to, and we want to be able to map the labels to that - not over 10 entries but over hundreds, or thousands, or hundreds of thousands. Tries are a great way of doing that: we treat the codes as keys and the full facility names as values. So let’s make a trie to do this matching, and then, well, match:

    library(triebeard)
    trie <- trie(keys = c("AO", "AEO", "AAI", "AFT", "QZ", "RF"),
                 values = c("Audobon", "Atlanta", "Ann Arbor", "Austin", "Queensland", "Raleigh"))

    longest_match(trie = trie, to_match = labels)

     [1] "Audobon"    "Atlanta"    "Ann Arbor"  "Austin"     "Queensland" "Queensland" "Raleigh"    "Audobon"    "Austin"
    [10] "Queensland"

This pulls out, for each label, the trie value where the associated key has the longest prefix-match to the label. We can also just grab all the values where the key starts with, say, A:

    prefix_match(trie = trie, to_match = "A")

    [[1]]
    [1] "Ann Arbor" "Atlanta"   "Austin"    "Audobon"

And finally if we want we can match very, very fuzzily using “greedy” matching:

    greedy_match(trie = trie, to_match = "AO")

    [[1]]
    [1] "Ann Arbor" "Atlanta"   "Austin"    "Audobon"

These operations are very, very efficient. If we use longest-match as an example, since that’s the most useful thing, with a one-million element vector of things to match against:

    library(triebeard)
    library(microbenchmark)

    trie <- trie(keys = c("AO", "AEO", "AAI", "AFT", "QZ", "RF"),
                 values = c("Audobon", "Atlanta", "Ann Arbor", "Austin", "Queensland", "Raleigh"))

    labels <- rep(c("AO-1002", "AEO-1004", "AAI-1009", "AFT-1403", "QZ-9065", "QZ-1021", "RF-0901",
                    "AO-1099", "AFT-1101", "QZ-4933"), 100000)

    microbenchmark({longest_match(trie = trie, to_match = labels)})

    Unit: milliseconds
                                                      expr      min       lq     mean   median       uq      max neval
     {     longest_match(trie = trie, to_match = labels) } 284.6457 285.5902 289.5342 286.8775 288.4564 327.3878   100

I think we can call <300 milliseconds for a million matches against an entire set of possible values pretty fast.

## Radix modification

There’s always the possibility that (horror of horrors) you’ll have to add or remove entries from the trie. Fear not; you can do just that with `trie_add` and `trie_remove` respectively, both of which silently modify the trie they’re provided with to add or remove whatever key-value pairs you provide:

    to_match = "198.0.0.1"
    trie_inst <- trie(keys = "197", values = "fake range")

    longest_match(trie_inst, to_match)
    [1] NA

    trie_add(trie_inst, keys = "198", values = "home range")
    longest_match(trie_inst, to_match)
    [1] "home range"

    trie_remove(trie_inst, keys = "198")
    longest_match(trie_inst, to_match)
    [1] NA

## Metadata and coercion

You can also extract information from tries without using them. `dim`, `str`, `print` and `length` all work for tries, and you can use `get_keys(trie)` and `get_values(trie)` to extract, respectively, the keys and values from a trie object.

In addition, you can also coerce tries into other R data structures, specifically lists and data.frames:

    trie <- trie(keys = c("AO", "AEO", "AAI", "AFT", "QZ", "RF"),
                 values = c("Audobon", "Atlanta", "Ann Arbor", "Austin", "Queensland", "Raleigh"))

    str(as.data.frame(trie))
    'data.frame':   6 obs. of  2 variables:
     $ keys  : chr  "AAI" "AEO" "AFT" "AO" ...
     $ values: chr  "Ann Arbor" "Atlanta" "Austin" "Audobon" ...

    str(as.list(trie))

    List of 2
     $ keys  : chr [1:6] "AAI" "AEO" "AFT" "AO" ...
     $ values: chr [1:6] "Ann Arbor" "Atlanta" "Austin" "Audobon" ...

### Other trie operations

If you have ideas for other trie-like structures, or functions that would be useful with these tries, the best approach is to either request it or add it!