Finding overlapping intervals using SQL

Question

I want to extract rows from a table whose interval intersects with an interval specified in the query. Assuming that I have a simple ID, DATE_START, DATE_END table and two query parameters P_DATE_START and P_DATE_END, what is the simplest way of expressing the query so that I find all rows for which [DATE_START, DATE_END] has at least one common element with [P_DATE_START, P_DATE_END]?

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Update:

To make the desired outcome clearer, please find a list of input values and expected outcomes below. Colums are DATE_START, DATE_END, P_DATE_START, P_DATE_END, MATCH.

16, 17, 15, 18, YES
15, 18, 16, 17, YES
15, 17, 16, 18, YES
16, 18, 15, 17, YES
16, 17, 18, 19, NO
18, 19, 16, 17, NO

Answer 1

Even simpler:

SELECT id, date_start, date_end 
FROM thetable 
WHERE date_start <= p_date_end 
AND date_end >= p_date_start