Speed up construction of universe from IntervalSets #21
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Add check that creating a new IntervalSet from a list of 2 intervals is equivalent to taking the union of those 2 intervals.
set_cover.approx_multiuniverse() constructs the universes by taking the union over all input sets. When use_intervalsets is True, this was previously slow. (use_intervalsets is True for most runs because set_cover_filter sets it to True.) It worked by creating an empty IntervalSet, and then repeatedly taking the union of the universe's IntervalSet with another input set (also represented as an IntervalSet). In the worst-case, taking the union takes O(n) time where n is the current size of the universe. As a result, constructing the universe took, in the worst-case, O(n^2) time. For particularly long genomes, where n is large, this could take hours in practice. This fix instead initializes each universe by simply constructing a list of the input intervals for it, and then initializing an IntervalSet from the list. Initializing the IntervalSet already merges overlapping intervals (effectively taking the union of all of them) in O(N log N) time, where N is the number of input intervals. Since the input sets are constructed from the universe, N is O(n), where n is defined above. So, now, constructing the universe takes, in the worst-case, O(n log n) time. In practice, this seems to provide a noticeable speed up as well.
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set_cover.approx_multiuniverse()constructs the universes by takingthe union over all input sets. When
use_intervalsetsis True,this was previously slow. (
use_intervalsetsis True for most runs becauseset_cover_filtersets it to True.) It worked by creating an emptyIntervalSet, and then repeatedly taking the union of the universe's
IntervalSet with another input set (also represented as an IntervalSet).
In the worst-case, taking the union takes O(n) time where n is the
current size of the universe. As a result, constructing the universe
took, in the worst-case, O(n^2) time. For particularly long genomes,
where n is large, this could take hours in practice.
This fix instead initializes each universe by simply constructing
a list of the input intervals for it, and then initializing an IntervalSet
from the list. Initializing the IntervalSet already merges overlapping
intervals (effectively taking the union of all of them) in O(N log N)
time, where N is the number of input intervals. Since the input sets
are constructed from the universe, N is O(n), where n is defined above.
So, now, constructing the universe takes, in the worst-case, O(n log n)
time. In practice, this seems to provide a noticeable speed up as well.