Question

I have a massive (~10⁹) set of events characterized by a start and end time. Given a time, I want to find how many on those events were ongoing at that time.

What sort of data structure would be helpful in this situation? The operations I need to be fast are:

1. Inserting new events, e.g., {start: 100000 milliseconds, end: 100010 milliseconds}.
2. Querying the number of concurrent events at a given time.

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Update: Someone put a computational geometry flag on this, so I figure I should rephrase this in terms of computational geometry. I have a set of 1-dimensional intervals and I want to calculate how many of those intervals intersect with a given point. Insertion of new intervals must be fast.

Answer 1

You’re looking for an interval tree.

• Construction: O(n log n), where n is the number of intervals
• Query: O(m+log n), where m is the number of query results and n is the number of intervals
• Space: O(n)