The Nested Containment List is a datastructure for interval overlap queries, like the interval tree. It is usually an order of magnitude faster than the interval tree both for building and query lookups.
The implementation here is a revived version of the one used in the now defunct PyGr library, which died of bitrot. I have made it less memory-consuming and created wrapper functions which allows batch-querying the NCLS for further speed gains.
It was implemented to be the cornerstone of the PyRanges project, but I have made it available to the Python community as a stand-alone library. Enjoy.
Original Paper: https://academic.oup.com/bioinformatics/article/23/11/1386/199545 Cite: http://dx.doi.org/10.1093/bioinformatics/btz615
If you use this library in published research cite
http://dx.doi.org/10.1093/bioinformatics/btz615
pip install ncls
from ncls import NCLS
import pandas as pd
starts = pd.Series(range(0, 5))
ends = starts + 100
ids = starts
subject_df = pd.DataFrame({"Start": starts, "End": ends}, index=ids)
print(subject_df)
# Start End
# 0 0 100
# 1 1 101
# 2 2 102
# 3 3 103
# 4 4 104
ncls = NCLS(starts.values, ends.values, ids.values)
# python API, slower
it = ncls.find_overlap(0, 2)
for i in it:
print(i)
# (0, 100, 0)
# (1, 101, 1)
starts_query = pd.Series([1, 3])
ends_query = pd.Series([52, 14])
indexes_query = pd.Series([10000, 100])
query_df = pd.DataFrame({"Start": starts_query.values, "End": ends_query.values}, index=indexes_query.values)
query_df
# Start End
# 10000 1 52
# 100 3 14
# everything done in C/Cython; faster
l_idxs, r_idxs = ncls.all_overlaps_both(starts_query.values, ends_query.values, indexes_query.values)
l_idxs, r_idxs
# (array([10000, 10000, 10000, 10000, 10000, 100, 100, 100, 100,
# 100]), array([0, 1, 2, 3, 4, 0, 1, 2, 3, 4]))
print(query_df.loc[l_idxs])
# Start End
# 10000 1 52
# 10000 1 52
# 10000 1 52
# 10000 1 52
# 10000 1 52
# 100 3 14
# 100 3 14
# 100 3 14
# 100 3 14
# 100 3 14
print(subject_df.loc[r_idxs])
# Start End
# 0 0 100
# 1 1 101
# 2 2 102
# 3 3 103
# 4 4 104
# 0 0 100
# 1 1 101
# 2 2 102
# 3 3 103
# 4 4 104
# return intervals in python (slow/mem-consuming)
intervals = ncls.intervals()
intervals
# [(0, 100, 0), (1, 101, 1), (2, 102, 2), (3, 103, 3), (4, 104, 4)]There is also an experimental floating point version of the NCLS called FNCLS. See the examples folder.
Test file of 100 million intervals (created by subsetting gencode gtf with replacement):
| Library | Function | Time (s) | Memory (GB) |
|---|---|---|---|
| bx-python | build | 161.7 | 2.5 |
| ncls | build | 3.15 | 0.5 |
| bx-python | overlap | 148.4 | 4.3 |
| ncls | overlap | 7.2 | 0.5 |
Building is 50 times faster and overlap queries are 20 times faster. Memory usage is one fifth and one ninth.
Alexander V. Alekseyenko, Christopher J. Lee; Nested Containment List (NCList): a new algorithm for accelerating interval query of genome alignment and interval databases, Bioinformatics, Volume 23, Issue 11, 1 June 2007, Pages 1386–1393, https://doi.org/10.1093/bioinformatics/btl647