COITrees: Cache Oblivious Interval Trees

COITrees implements a data structure for very fast overlap queries of a static set of integer intervals, with genomic intervals in mind.

Borrowing from cgranges, this data structure stores intervals in contiguous memory, but improves query performance by storing the nodes in in-order van Emde Boas layout. Computing the layout requires some extra time and memory, but improves average cache locality for queries of the tree. If the interval set is relatively large, and a sufficiently large number of queries are performed, it tends to out-perform other data structures.

The SortedQuerent type implements an alternative query strategy that keeps track of the results of the previous query. When a query overlaps the previous one, the results from that previous query can be reused to dramatically accelerate the current one. (In the benchmarks, this is the --sorted option.)

Some operations can further be sped up using SIMD instructions. Two COITree variants are implemented to exploit AVX2 instructions on x86-64 cpus (AVXCOITree), and Neon instructions on ARM cpus (NeonCOITree). The COITree type is oppurtunistically defined to one of these types if the right instruction set is detected. Typically it's necessary to compile with the environment variable RUSTFLAGS="-Ctarget-cpu=native" set for this to work. The fallback implemntation (BasicCOITree) supports any platform rust compiles to and remains highly efficient.

Trying Out

This is primary a library for use in other programs, but for benchmarking purposes it includes a program for intersecting BED files.

To try out, just clone this repo and run:

cargo run --release --example bed-intersect -- test1.bed test2.bed > intersections.bed

Benchmarks

A is 2,755,864 intervals from Ensembl's human genome annotations, B is 62,159,484 intervals from some RNA-Seq alignments, and B' is the first 2 million lines of B.

Intervals in sorted order

	A vs B	B vs A	A vs A	B' vs B'
coitrees AVX	11.8s	3.7s	0.7	5.3s
coitrees AVX (--sorted)	6.4s	4.2s	0.6s	0.5s
coitrees	11.4s	5.2s	0.8s	8.3s
coitrees (--sorted)	5.8s	5.4s	0.6s	0.5s
cgranges (bedcov-cr -c)	35.4s	6.6s	2.0s	17.6s
AIList	13.8s	10.1s	1.1s	18.4s
CITree	20.1s	13.5s	1.6s	45.7s
NCList	22.5s	16.8s	1.9s	39.8s
AITree	23.8s	26.3s	2.1s	63.4s
bedtools coverage -counts -sorted	257.5s	295.6s	71.6s	2130.9s
bedtools coverage -counts	322.4s	378.5s	75.0s	3595.9s

With coverage

	A vs B	B vs A	A vs A	B' vs B'
coitrees AVX	18.2s	4.8s	1.1s	16.0s
coitrees	14.6s	5.7s	1.0s	12.0s
cgranges	38.4s	8.1s	2.2s	31.0s
CITree	23.2s	25.6s	2.0s	160.4s

Intervals in randomized order

	A vs B	B vs A	A vs A	B' vs B'
coitrees AVX	23.9s	7.2s	1.6s	6.1s
coitrees	24.2s	8.9s	1.9s	9.4s
cgranges (bedcov-cr -c)	55.7s	11.1s	3.3s	19.6s
AIList	31.2s	18.2s	2.3s	19.3s
CITree	39.4s	19.0s	2.9s	47.1s
NCList	42.7s	23.8s	3.4s	44.0s
AITree	225.3s	134.8s	14.7s	921.6s
bedtools coverage -counts	1160.4s	849.6s	104.5s	9254.6s

With coverage

	A vs B	B vs A	A vs A	B' vs B'
coitrees AVX	34.3s	8.8s	2.2s	16.3s
coitrees	29.6s	9.7s	2.3s	13.1s
cgranges	57.6s	12.5s	3.6s	32.6s
CITree	50.0s	32.5s	3.8s	170.4s

All benchmarks run on a ryzen 5950x.

Discussion

These benchmarks are somewhat realistic in that they use real data, but are not entirely apples-to-apples because they all involve parsing and writing BED files. Most of the programs (including the one implemented in coitrees) have incomplete BED parsers, and some use other shortcuts like assuming a fixed set of chromosomes with specific naming schemes.

bedtools carries the disadvantage of being an actually useful tool, rather than implemented being implemented entirely for the purpose of winning benchmark games. It seems clear it could be a lot faster, but there no doubt some cost can be chalked up to featurefulness, completeness, and safety.

If you have a BED intersection program you suspect may be faster (or just interesting), please let me know and I'll try to benchmark it.