  Efficient large-scale annotation of genomic intervals is essential for
personal genome interpretation in the realm of precision medicine. There are 13
possible relations between two intervals according to Allen's interval algebra.
Conventional interval trees are routinely used to identify the genomic
intervals satisfying a coarse relation with a query interval, but cannot
support efficient query for more refined relations such as all Allen's
relations. We design and implement a novel approach to address this unmet need.
Through rewriting Allen's interval relations, we transform an interval query to
a range query, then adapt and utilize the range trees for querying. We
implement two types of range trees: a basic 2-dimensional range tree (2D-RT)
and an augmented range tree with fractional cascading (RTFC) and compare them
with the conventional interval tree (IT). Theoretical analysis shows that RTFC
can achieve the best time complexity for interval queries regarding all Allen's
relations among the three trees. We also perform comparative experiments on the
efficiency of RTFC, 2D-RT and IT in querying noncoding element annotations in a
large collection of personal genomes. Our experimental results show that 2D-RT
is more efficient than IT for interval queries regarding most of Allen's
relations, RTFC is even more efficient than 2D-RT. The results demonstrate that
RTFC is an efficient data structure for querying large-scale datasets regarding
Allen's relations between genomic intervals, such as those required by
interpreting genome-wide variation in large populations.
