indexset

A pure-Rust two-level dynamic order-statistic b-tree.

This crate implements a compact set data structure that preserves its elements' sorted order and allows lookups of entries by value or sorted order position.

Also, it is(mostly) a drop-in replacement for the stdlib BTree.

Background

This was heavily inspired by indexmap, and python's sortedcontainers.

It differs from both in that:

• indexmap is a hashmap that provides numerical lookups, but does not maintain order in case of removals, while indexset is a b-tree that always maintains order, irrespective of which mutating operation is run.
• sortecontainers is similar in spirit, but utilizes a different routine for balancing the tree, and relies on a heap for numerical lookups.

indexset provides the following features:

• As fast to iterate as a vec.
• Zero indirection.
• Lookups by position and range.
• Minimal amount of allocations.
• select(lookups by position) and rank operations in near constant time.

Performance

BTreeSet and BTreeMap derive a couple of performance facts directly from how it is constructed, which is roughly:

A two-level B-Tree with a fenwick tree as a low-cost index for numerical lookups

• Iteration is very fast since it inherits a vec's iter struct.
• Insertions and removals are constant time in the best-case scenario, and logarithmic on the node size in the worst case
• Lookups are very fast, and rely only on two binary searches over very little data.

Benchmarks

run cargo bench and see it for yourself.

On a lowest-specced M1 macbook pro I got the following numbers:

Inserting 100k random usize

• stdlib::collections::BTreeSet.insert(i): 8.25ms
• indexset::BTreeSet.insert(i): 17.3ms

Checking that each 100k random usize integers exist

• stdlib::collections::BTreeSet.contains(i): 7.5ms
• indexset::BTreeSet.contains(i): 6.8ms

Getting all 100k i-th elements

• stdlib::collections::BTreeSet.iter.nth(i): 13.28s yes, seconds!
• indexset::BTreeSet.get_index(i): 3.93ms

Iterating over all 100k elements and then collecting it into a vec

• Vec::from_iter(stdlib::collections::BTreeSet.iter()): 227.28us
• Vec::from_iter(indexset::BTreeSet.iter()): 123.21.us

Yes.

Getting the i-th element is 3400x faster than stdlib's btree, contains is 10% faster, and iterating is twice as fast, at the cost of insertions being half as fast.

If your use case of std::collections::BTreeSet and BTreeMap is more read-heavy, or if you really need to index by sorted-order position, it might be worth checking out this indexset instead.

Limitations

• BTreeMap is less polished than BTreeSet. This crate has been optimised for a leaner BTreeSet.
• This is beta quality software, so use it at your own risk. I'm not 100% certain about every single iterator implementation(everything has tests though).
• There's quite a couple utility traits that have not been implemented yet.

Naming

This library is called indexset, because the base data structure is BTreeSet. BTreeMap is a BTreeSet with a Pair<K, V> item type.

Changelog

See CHANGELOG.md.