Fig. 1.

Comparing a naïve binary search for interval intersection to the BITS approach. (A) Binary searches of intervals sorted by start coordinate will occasionally identify overlapping intervals. However, contained intervals prevent knowing how far one must scan the database to identify all intersections. (B) Contained intervals also cause single binary searches to falsely conclude that no intersections exist for a given query interval. (C) To overcome these limitations, BITS uses two binary searches of the database intervals: one into a sorted list of end coordinates and the other into a sorted list of start coordinates. Each search excludes database intervals that cannot intersect the query, leaving solely the intervals that must intersect the query