How can I select the nearest value less-than and greater-than a given value efficiently?

Question

I have two tables, one for values one for location and am trying to interpolate location. The tables have been simplified to the following:

CREATE TABLE value(
    Timestamp DATETIME2,
    Value float NOT NULL,
    PRIMARY KEY(Timestamp)
);

CREATE TABLE location(
    Timestamp DATETIME2,
    Position INT NOT NULL,
    PRIMARY KEY(Timestamp)
); 

INSERT INTO value VALUES 
    ('2011/12/1 16:55:01', 1),
    ('2011/12/1 16:55:02', 5),
    ('2011/12/1 16:55:05', 10),
    ('2011/12/1 16:55:08', 6);

INSERT INTO location VALUES 
    ('2011/12/1 16:55:00', 0),
    ('2011/12/1 16:55:05', 10),
    ('2011/12/1 16:55:10', 5)

The expected results would be

TimeStamp, Value, LowerTime, LowerLocation, UpperTime, UpperLocation
2011-12-01 16:55:01,  1, 2011-12-01 16:55:00,  0, 2011-12-01 16:55:05, 10
2011-12-01 16:55:02,  5, 2011-12-01 16:55:00,  0, 2011-12-01 16:55:05, 10
2011-12-01 16:55:05, 10, 2011-12-01 16:55:05, 10, 2011-12-01 16:55:05, 10
2011-12-01 16:55:08,  6, 2011-12-01 16:55:05, 10, 2011-12-01 16:55:10,  5

(Keep in mind this is simplified sample data to get the idea of the query I am trying to perform across.)

To do the interpolation, I need to figure out the time and locations before and after a given values time. I am currently doing this with a query that looks like:

SELECT 
    V.Timestamp, 
    V.Value, 
    (SELECT MAX(Timestamp) FROM dbo.location WHERE Timestamp <= V.Timestamp) as LowerTime,
    (SELECT TOP 1 Position FROM dbo.location WHERE Timestamp <= V.Timestamp ORDER BY timestamp DESC) as LowerLocation,
    (SELECT MIN(Timestamp) FROM dbo.location WHERE Timestamp >= V.Timestamp) as UpperTime,
    (SELECT TOP 1 Position FROM dbo.location WHERE Timestamp >= V.Timestamp ORDER BY timestamp ASC) as UpperLocation
 FROM 
    dbo.value V 

Now this works, but this obviously is doing a lot of work. I'm thinking there must be a query simplification that I'm missing but I've been playing with it all morning and haven't come up with anything concrete. Hoping someone here has a better idea.

I am currently exploring if there is a way to figure out the LowerTime and UpperTime and use those in determining the Locations. Something like:

SELECT 
    V.Timestamp, 
    V.Value, 
    (SELECT MAX(Timestamp) FROM dbo.location WHERE Timestamp <= V.Timestamp) as LowerTime,
    (SELECT Position FROM dbo.location WHERE Timestamp = LowerTime) as LowerLocation,
    (SELECT MIN(Timestamp) FROM dbo.location WHERE Timestamp >= V.Timestamp) as UpperTime,
    (SELECT Position FROM dbo.location WHERE Timestamp = UpperTime) as UpperLocation
 FROM 
    dbo.value V 

but this doesn't work.

EDIT1: Updated query as suggested. However no visible change in execution time.

EDIT2: Added my thoughts of the approach I am currently trying.

Answer 1

For simplicity you may at least use MAX() and MIN() functions for querying timestamp field instead of TOP 1 and ORDER BY .

Full query will be

SELECT 
    V.Timestamp, 
    V.Value, 
    (SELECT MAX(Timestamp) FROM dbo.location WHERE Timestamp <= V.Timestamp) as LowerTime,
    (SELECT TOP 1 Position FROM dbo.location WHERE Timestamp <= V.Timestamp ORDER BY timestamp DESC) as LowerLocation,
    (SELECT MIN(Timestamp) FROM dbo.location WHERE Timestamp >= V.Timestamp) as UpperTime,
    (SELECT TOP 1 Position FROM dbo.location WHERE Timestamp >= V.Timestamp ORDER BY timestamp ASC) as UpperLocation
 FROM 
    dbo.value V 

Answer 2

This might do the trick (although I think the join looks quite ugly):

;with OrderedLocations as (
    select
        v.Timestamp,
        v.Value,
        l.Timestamp as tsl,
        l.Position,
        ROW_NUMBER() OVER (PARTITION BY v.Timestamp ORDER BY CASE WHEN l.Timestamp <= v.Timestamp THEN l.Timestamp ELSE '00010101' END desc) as PrevRN,
        ROW_NUMBER() OVER (PARTITION BY v.Timestamp ORDER BY CASE WHEN l.Timestamp >= v.Timestamp THEN l.Timestamp ELSE '99991231' END asc) as NextRN
    from
        value v
            cross join
        location l
)
select
    ol1.Timestamp,
    ol1.Value,
    ol1.tsl,
    ol1.Position,
    ol2.tsl,
    ol2.Position
from
    OrderedLocations ol1
        inner join
    OrderedLocations ol2
        on
            ol1.Timestamp = ol2.Timestamp and
            ol1.Value = ol2.Value
where
    ol1.PrevRN = 1 and
    ol2.NextRN = 1

Unfortunately, as with most efficiency/performance questions, the answer tends to be try lots of different combinations with your actual tables and data, and measure how each one performs.

---

An alternative (avoiding the join) using the same CTE as above would be:

SELECT Timestamp,Value,
    MAX(CASE WHEN PrevRN=1 THEN tsl END),MAX(CASE WHEN PrevRN=1 then Position END),
    MAX(CASE WHEN NextRN=1 THEN tsl END),MAX(CASE WHEN NextRN=1 then Position END)
FROM
    OrderedLocations
where PrevRN=1 or NextRN=1
group by Timestamp,Value

---

The CTE ( OrderedLocations ) is trying to construct a rowset where every row from location is matched to every row in value . For each resulting row, we calculate two ROW_NUMBER s - the row number where we number all rows with a lower or equal timestamp ( PrevRN ) in descending order, and another where we number all rows with a greater or equal timestamp ( NextRN ) ascending. We then construct our final result by just considering those rows where one of those row numbers is 1.