Mutable, self-balancing interval tree

interval-tree, data-structure, intervals, tree
pip install PyIntervalTree==0.5



NB: This package is deprecated. Please, use the intervaltree package instead (available via Github or PyPI).

The genome-related functionality is extracted to the intervaltree-bio package (Github, PyPI).

No future versions of this package are planned. Do not file issues.

A mutable, self-balancing interval tree. Queries may be by point, by range overlap, or by range envelopment.

This library was designed to allow tagging text and time intervals, where the intervals include the lower bound but not the upper bound.


The easiest way to install most Python packages is via easy_install or pip:

$ pip install PyIntervalTree


  • Initialize blank or from an iterable of Intervals in O(n * log n).
  • Insertions
    • tree[begin:end] = data
    • tree.add(interval)
    • tree.addi(begin, end, data)
    • tree.extend(list_of_interval_objs)
  • Deletions
    • tree.remove(interval) (raises ValueError if not present)
    • tree.discard(interval) (quiet if not present)
    • tree.removei(begin, end, data)
    • tree.discardi(begin, end, data)
    • tree.remove_overlap(point)
    • tree.remove_overlap(begin, end) (removes all overlapping the range)
    • tree.remove_envelop(begin, end) (removes all enveloped in the range)
  • Overlap queries:
    • tree[point]
    • tree[begin:end]
    •, end)
  • Envelop queries:
    •, end, strict = True)
  • Membership queries:
    • interval_obj in tree (this is fastest, O(1))
    • tree.containsi(begin, end, data)
    • tree.overlaps(point)
    • tree.overlaps(begin, end)
  • Iterable:
    • for interval_obj in tree:
    • tree.items()
  • Sizing:
    • len(tree)
    • tree.is_empty()
    • not tree
    • tree.begin() (the smallest coordinate of the leftmost interval)
    • tree.end() (the end coordinate of the rightmost interval)
  • Restructuring
    • split_overlaps()
  • Copy- and typecast-able:
    • IntervalTree(tree) (Interval objects are same as those in tree)
    • tree.copy() (Interval objects are shallow copies of those in tree)
    • set(tree) (can later be fed into IntervalTree())
    • list(tree) (ditto)
  • Equal-able
  • Pickle-friendly
  • Automatic AVL balancing


  • Getting started:

    from intervaltree import Interval, IntervalTree
    t = IntervalTree()
  • Adding intervals - you don't have to use strings!:

    t[1:2] = "1-2"
    t[4:7] = "4-7"
    t[5:9] = "5-9"
  • Query by point:

    ivs = t[6]            # set([Interval(4, 7, '4-7'), Interval(5, 9, '5-9')])
    iv = sorted(ivs)[0]   # Interval(4, 7, '4-7')
  • Accessing an Interval object:

    iv.begin  # 4
    iv.end    # 7   # "4-7"
  • Query by range:

    Note that ranges are inclusive of the lower limit, but non-inclusive of the upper limit. So:

    t[2:4]    # set([])


    t[1:5]    # set([Interval(1, 2, '1-2'), Interval(4, 7, '4-7')])
  • Constructing from lists of Interval's:

    We could have made the same tree this way:

    ivs = [ [1,2], [4,7], [5,9] ]
    ivs = map( lambda begin,end: Interval(begin, end, "%d-%d" % (begin,end),
               *zip(*ivs) )
    t = IntervalTree(ivs)
  • Removing intervals:

    t.remove( Interval(1, 2, "1-2") )
    list(t)     # [Interval(4, 7, '4-7'), Interval(5, 9, '5-9')]
    t.remove( Interval(500, 1000, "Doesn't exist") # raises ValueError
    t.discard(Interval(500, 1000, "Doesn't exist") # quietly does nothing
    list(t)     # []

    We could also empty a tree by removing all intervals, from the lowest bound to the highest bound of the IntervalTree:

    t.remove_overlap(t.begin(), t.end())

Usage with Genomic Data

Interval trees are especially commonly used in bioinformatics, where intervals correspond to genes or various features along the genome. Such intervals are commonly stored in BED-format files. To simplify working with such data, the package provides a GenomeIntervalTree class.

GenomeIntervalTree is essentially a dict of IntervalTree-s, indexed by chromosome names:

gtree = GenomeIntervalTree()
gtree['chr1'].addi(10000, 20000)

There is a convenience function for adding intervals:

gtree.addi('chr2', 20000, 30000)

You can create a GenomeIntervalTree instance from a BED file:

test_url = ''
data = zlib.decompress(urlopen(test_url).read(), 16+zlib.MAX_WBITS)
gtree = GenomeIntervalTree.from_bed(StringIO(data))

In addition, special functions are offered to read in UCSC tables of gene positions:

  • Load the UCSC knownGene table with each interval corresponding to gene's transcribed region:

    knownGene = GenomeIntervalTree.from_table()
  • Load the UCSC refGene table with each interval corresponding to gene's coding region:

    url = ''
    refGene = GenomeIntervalTree.from_table(url=url, parser=UCSCTable.REF_GENE, mode='cds')
  • Load the UCSC ensGene table with each interval corresponding to a gene's exon:

    url = ''
    ensGene = GenomeIntervalTree.from_table(url=url, parser=UCSCTable.ENS_GENE, mode='exons')

You may add methods for parsing your own tabular files with genomic intervals, see the documentation for GenomeIntervalTree.from_table.

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