AsterixDB supports Allen's relations over interval types. Allen's relations are also called Allen's interval algebra. There are totally 13 base relations described by this algebra, and all of them are supported in AsterixDB (note that interval-equals is supported by the = comparison symbol so there is no extra function for it).
A detailed description of Allen's relations can be found from its wikipedia entry.
Syntax:
interval-before(interval1, interval2) interval-after(interval1, interval2)
These two functions check whether an interval happens before/after another interval.
Arguments:
interval1, interval2: two intervals to be comparedReturn Value:
A boolean value. Specifically, interval-before(interval1, interval2) is true if and only if interval1.end < interval2.start, and interval-after(interval1, interval2) is true if and only if interval1.start > interval2.end. If any of the two inputs is null, null is returned.
Examples:
let $itv1 := interval(date("2000-01-01"), date("2005-01-01"))
let $itv2 := interval(date("2005-05-01"), date("2012-09-09"))
return {"interval-before": interval-before($itv1, $itv2), "interval-after": interval-after($itv2, $itv1)}
The expected result is:
{ "interval-before": true, "interval-after": true }
Syntax:
interval-covers(interval1, interval2) interval-covered-by(interval1, interval2)
These two functions check whether one interval covers the other interval.
Arguments:
interval1, interval2: two intervals to be comparedReturn Value:
A boolean value. Specifically, interval-covers(interval1, interval2) is true if and only if
interval1.start <= interval2.start AND interval1.end >= interval2.end
interval-covered-by(interval1, interval2) is true if and only if
interval2.start <= interval1.start AND interval2.end >= interval1.end
For both functions, if any of the two inputs is null, null is returned.
Examples:
let $itv1 := interval(date("2000-01-01"), date("2005-01-01"))
let $itv2 := interval(date("2000-03-01"), date("2004-09-09"))
let $itv3 := interval(date("2006-08-01"), date("2007-03-01"))
let $itv4 := interval(date("2004-09-10"), date("2012-08-01"))
return {"interval-covers": interval-covers($itv1, $itv2), "interval-covered-by": interval-covered-by($itv3, $itv4)}
The expected result is:
{ "interval-covers": true, "interval-covered-by": true }
Syntax:
interval-overlaps(interval1, interval2) interval-overlapped-by(interval1, interval2)
These functions check whether two intervals overlap with each other.
Arguments:
interval1, interval2: two intervals to be comparedReturn Value:
A boolean value. Specifically, interval-overlaps(interval1, interval2) is true if and only if
interval1.start < interval2.start AND interval2.end > interval1.end AND interval1.end > interval2.start
interval-overlapped-by(interval1, interval2) is true if and only if
interval2.start < interval1.start AND interval1.end > interval2.end AND interval2.end > interval1.start
For all these functions, if any of the two inputs is null, null is returned.
Note that interval-overlaps and interval-overlapped-by are following the Allen's relations on the definition of overlap.
Examples:
let $itv1 := interval(date("2000-01-01"), date("2005-01-01"))
let $itv2 := interval(date("2004-05-01"), date("2012-09-09"))
let $itv3 := interval(date("2006-08-01"), date("2007-03-01"))
let $itv4 := interval(date("2004-09-10"), date("2006-12-31"))
return {"overlaps": interval-overlaps($itv1, $itv2),
"overlapped-by": interval-overlapped-by($itv3, $itv4)}
The expected result is:
{ "overlaps": true, "overlapped-by": true }
Note that interval-overlapping is not an Allen's Relation, but syntactic sugar we added for the case that the intersect of two intervals is not empty. Basically this function returns true if any of these functions return true: interval-overlaps, interval-overlapped-by, interval-covers, or interval-covered-by.
Syntax:
interval-overlapping(interval1, interval2)
This functions check whether two intervals share any points with each other.
Arguments:
interval1, interval2: two intervals to be comparedReturn Value:
A boolean value. Specifically, interval-overlapping(interval1, interval2) is true if
(interval2.start >= interval1.start AND interval2.start < interval1.end) OR (interval2.end > interval1.start AND interval2.end <= interval1.end)
If any of the two inputs is null, null is returned.
Examples:
let $itv1 := interval(date("2000-01-01"), date("2005-01-01"))
let $itv2 := interval(date("2004-05-01"), date("2012-09-09"))
let $itv3 := interval(date("2006-08-01"), date("2007-03-01"))
let $itv4 := interval(date("2004-09-10"), date("2006-12-31"))
return {"overlapping1": interval-overlapping($itv1, $itv2),
"overlapping2": interval-overlapping($itv3, $itv4)}
The expected result is:
{ "overlapping1": true, "overlapping2": true }
Syntax:
interval-meets(interval1, interval2) interval-met-by(interval1, interval2)
These two functions check whether an interval meets with another interval.
Arguments:
interval1, interval2: two intervals to be comparedReturn Value:
A boolean value. Specifically, interval-meets(interval1, interval2) is true if and only if interval1.end = interval2.start, and interval-met-by(interval1, interval2) is true if and only if interval1.start = interval2.end. If any of the two inputs is null, null is returned.
Examples:
let $itv1 := interval(date("2000-01-01"), date("2005-01-01"))
let $itv2 := interval(date("2005-01-01"), date("2012-09-09"))
let $itv3 := interval(date("2006-08-01"), date("2007-03-01"))
let $itv4 := interval(date("2004-09-10"), date("2006-08-01"))
return {"meets": interval-meets($itv1, $itv2), "metby": interval-met-by($itv3, $itv4)}
The expected result is:
{ "meets": true, "metby": true }
Syntax:
interval-starts(interval1, interval2) interval-started-by(interval1, interval2)
These two functions check whether one interval starts with the other interval.
Arguments:
interval1, interval2: two intervals to be comparedReturn Value:
A boolean value. Specifically, interval-starts(interval1, interval2) returns true if and only if
interval1.start = interval2.start AND interval1.end <= interval2.end
interval-started-by(interval1, interval2) returns true if and only if
interval1.start = interval2.start AND interval2.end <= interval1.end
For both functions, if any of the two inputs is null, null is returned.
Examples:
let $itv1 := interval(date("2000-01-01"), date("2005-01-01"))
let $itv2 := interval(date("2000-01-01"), date("2012-09-09"))
let $itv3 := interval(date("2006-08-01"), date("2007-03-01"))
let $itv4 := interval(date("2006-08-01"), date("2006-08-02"))
return {"interval-starts": interval-starts($itv1, $itv2), "interval-started-by": interval-started-by($itv3, $itv4)}
The expected result is:
{ "interval-starts": true, "interval-started-by": true }
Syntax:
interval-ends(interval1, interval2) interval-ended-by(interval1, interval2)
These two functions check whether one interval ends with the other interval.
Arguments:
interval1, interval2: two intervals to be comparedReturn Value:
A boolean value. Specifically, interval-ends(interval1, interval2) returns true if and only if
interval1.end = interval2.end AND interval1.start >= interval2.start
interval-ended-by(interval1, interval2) returns true if and only if
interval2.end = interval1.end AND interval2.start >= interval1.start
For both functions, if any of the two inputs is null, null is returned.
Examples:
let $itv1 := interval(date("2000-01-01"), date("2005-01-01"))
let $itv2 := interval(date("1998-01-01"), date("2005-01-01"))
let $itv3 := interval(date("2006-08-01"), date("2007-03-01"))
let $itv4 := interval(date("2006-09-10"), date("2007-03-01"))
return {"interval-ends": interval-ends($itv1, $itv2), "interval-ended-by": interval-ended-by($itv3, $itv4) }
The expected result is:
{ "interval-ends": true, "interval-ended-by": true }