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