Abstract
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.
Highlights
To efficiently retrieve all the genomic intervals satisfying a certain Allen’s relation with a given genomic interval from a large dataset, we regarded an interval as a 2-dimensional point and transformed the interval query problem to the range query problem by rewriting the definition of Allen’s interval relations
We focus our analysis on annotating two types of genomic variants, of varying lengths: single nucleotide variants (SNVs) and insertions/deletions, both detected in the 123,136 exome sequences and the 15,496 whole-genome sequences of the gnomAD13
Our results show that the range tree data structure can be more efficient than an interval tree for the genomic interval queries in most cases, and the technique of fractional cascading can further improve the query efficiency for range trees
Summary
Efficient queries for genomic intervals that have a certain relation with a given interval are essential for various bioinformatic applications, especially for large genomic datasets. According to Allen’s interval algebra, there are 13 possible relations between two intervals, 11 out of which are associated with the intersection, the other two are associated with non-intersection. Though the coarse intersection query is widely studied, and the studies have made some achievements, interval queries regarding more refined relations are of interest. When applying existing interval query methods designed for the coarse intersection to a more refined relation in Allen’s algebra, they need to find all the intervals satisfying the coarse intersection relations, and search in the results for intervals satisfying the refined relation. Our objective is to improve the interval query efficiency regarding refined relations in Allen’s algebra using query rewriting and the range tree data structure. Our method can achieve the optimal O(logn + k) time complexity for interval queries regarding all Allen’s interval relations
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