IRanges (version 2.2.9)

IntervalTree-class: Interval Search Trees

Description

Efficiently perform overlap queries with an interval tree.

WARNING: IntervalTree objects are deprecated. Please use NCList objects instead. See ?NCList for more information.

Constructor

IntervalTree(ranges): Creates an IntervalTree from the ranges in ranges, an object coercible to IntervalTree, such as an IRanges object.

Coercion

as(from, "IRanges"): Imports the ranges in from, an IntervalTree, to an IRanges.

as(from, "IntervalTree"): Constructs an IntervalTree representing from, a Ranges object that is coercible to IRanges.

Accessors

length(x): Gets the number of ranges stored in the tree. This is a fast operation that does not bring the ranges into R.

start(x): Get the starts of the ranges.

end(x): Get the ends of the ranges.

Notes on Time Complexity

The cost of constructing an instance of the interval tree is a O(n*lg(n)), which makes it about as fast as other types of overlap query algorithms based on sorting. The good news is that the tree need only be built once per subject; this is useful in situations of frequent querying. Also, in this implementation the data is stored outside of R, avoiding needless copying. Of course, external storage is not always convenient, so it is possible to coerce the tree to an instance of IRanges (see the Coercion section). For the query operation, the running time is based on the query size m and the average number of hits per query k. The output size is then max(mk,m), but we abbreviate this as mk. Note that when the multiple parameter is set to FALSE, k is fixed to 1 and drops out of this analysis. We also assume here that the query is sorted by start position (the findOverlaps function sorts the query if it is unsorted). An upper bound for finding overlaps is O(min(mk*lg(n),n+mk)). The fastest interval tree algorithm known is bounded by O(min(m*lg(n),n)+mk) but is a lot more complicated and involves two auxillary trees. The lower bound is Omega(lg(n)+mk), which is almost the same as for returning the answer, Omega(mk). The average is of course somewhere in between. This analysis informs the choice of which set of ranges to process into a tree, i.e. assigning one to be the subject and the other to be the query. Note that if m > n, then the running time is O(m), and the total operation of complexity O(n*lg(n) + m) is better than if m and n were exchanged. Thus, for once-off operations, it is often most efficient to choose the smaller set to become the tree (but k also affects this). This is reinforced by the realization that if mk is about the same in either direction, the running time depends only on n, which should be minimized. Even in cases where a tree has already been constructed for one of the sets, it can be more efficient to build a new tree when the existing tree of size n is much larger than the query set of size m, roughly when n > m*lg(n).

Details

A common type of query that arises when working with intervals is finding which intervals in one set overlap those in another. An efficient family of algorithms for answering such queries is known as the Interval Tree. This implementation makes use of the augmented tree algorithm from the reference below, but heavily adapts it for the use case of large, sorted query sets.

The simplest approach for finding overlaps is to call the findOverlaps function on a Ranges or other object with range information. See the man page of findOverlaps for how to use this and other related functions.

An IntervalTree object is a derivative of Ranges and stores its ranges as a tree that is optimized for overlap queries. Thus, for repeated queries against the same subject, it is more efficient to create an IntervalTree once for the subject using the constructor described below and then perform the queries against the IntervalTree instance.

References

Interval tree algorithm from: Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford. Introduction to Algorithms, second edition, MIT Press and McGraw-Hill. ISBN 0-262-53196-8

See Also

findOverlaps for finding/counting interval overlaps between two "range-based" objects, Ranges, the parent of this class, Hits, set of hits between 2 vector-like objects.

Examples

if (interactive()) {
  ## IntervalTree objects are deprecated. Please use NCList objects
  ## instead. See ?NCList for more information.
  query <- IRanges(c(1, 4, 9), c(5, 7, 10))
  subject <- IRanges(c(2, 2, 10), c(2, 3, 12))
  tree <- IntervalTree(subject)

  findOverlaps(query, tree)

  ## query and subject are easily interchangeable
  query <- IRanges(c(1, 4, 9), c(5, 7, 10))
  subject <- IRanges(c(2, 2), c(5, 4))
  tree <- IntervalTree(subject)

  t(findOverlaps(query, tree))
  # the same as:
  findOverlaps(subject, query)
}