MySQL – How to Query for ‘First Showed Up As’

First things first, I notice that your 'what I do now' query:

SELECT TOP (1)
    ca.SensorValue,
    ca.Date
FROM sys.partitions AS p
CROSS APPLY
(
    SELECT TOP (1)
        v.Date, 
        v.SensorValue
    FROM SensorValues AS v
    WHERE 
        $PARTITION.SensorValues_Date_PF(v.Date) = p.[partition_number]
        AND v.DeviceId = @fDeviceId
        AND v.SensorId = @fSensorId
        AND v.Date <= @fDate
    ORDER BY 
        v.Date DESC
) AS ca
WHERE 
    p.[partition_number] <= $PARTITION.SensorValues_Date_PF(@fDate)
    AND p.[object_id] = OBJECT_ID(N'dbo.SensorValues', N'U')
    AND p.index_id = 1
ORDER BY
    p.[partition_number] DESC, 
    ca.Date DESC;

...produces an execution plan like this:

This execution plan has an estimated total cost of 0.02 units. Over 50% of this estimated cost is the final Sort, running in Top-N mode. Now estimates are just that, but sorts can be expensive in general, so let's remove it without changing the semantics:

SELECT TOP (1)
    ca.SensorId,
    ca.SensorValue,
    ca.Date
FROM
(
    -- Partition numbers
    SELECT DISTINCT
        partition_number = prv.boundary_id
    FROM
        sys.partition_functions AS pf
    JOIN sys.partition_range_values AS prv ON
        prv.function_id = pf.function_id
    WHERE
        pf.name = N'SensorValues_Date_PF'
        AND prv.boundary_id <= $PARTITION.SensorValues_Date_PF(@fDate)
) AS p
CROSS APPLY
    (
    SELECT TOP (1)
        v.Date,
        v.SensorValue,
        v.SensorId
    FROM dbo.SensorValues AS v
    WHERE
        $PARTITION.SensorValues_Date_PF(v.Date) = p.partition_number
        AND v.DeviceId = @fDeviceId
        AND v.SensorId = @fSensorId
        AND v.Date <= @fDate
    ORDER BY
        v.Date DESC
  ) AS ca
ORDER BY
    p.partition_number DESC,
    ca.Date DESC

Now the execution plan has no blocking operators, and no sorts in particular. The estimated cost of the new query plan below is 0.01 units and the total cost is distributed evenly over the data access methods:

With the improvement in place, all we need to produce a result for each Sensor ID is to make a list of Sensor IDs and APPLY the previous code to each one:

SELECT
    PerSensor.SensorId,
    PerSensor.SensorValue,
    PerSensor.Date
FROM 
(
    -- Sensor ID list
    VALUES 
        (@fSensorId1),
        (@FSensorId2),
        (@FSensorId3)
) AS Sensor (Id)
CROSS APPLY
(
    -- Optimized code applied to each sensor
    SELECT TOP (1)
        ca.SensorId,
        ca.SensorValue,
        ca.Date
    FROM
    (
        -- Partition numbers
        SELECT DISTINCT
            partition_number = prv.boundary_id
        FROM
            sys.partition_functions AS pf
        JOIN sys.partition_range_values AS prv ON
            prv.function_id = pf.function_id
        WHERE
            pf.name = N'SensorValues_Date_PF'
            AND prv.boundary_id <= $PARTITION.SensorValues_Date_PF(@fDate)
    ) AS p
    CROSS APPLY
        (
        SELECT TOP (1)
            v.Date,
            v.SensorValue,
            v.SensorId
        FROM dbo.SensorValues AS v
        WHERE
            $PARTITION.SensorValues_Date_PF(v.Date) = p.partition_number
            AND v.DeviceId = @fDeviceId
            AND v.SensorId = Sensor.Id--@fSensorId1
            AND v.Date <= @fDate
        ORDER BY
            v.Date DESC
      ) AS ca
    ORDER BY
        p.partition_number DESC,
        ca.Date DESC
) AS PerSensor;

The query plan is:

Estimated query plan cost for three Sensor IDs is 0.011 - half that of the original single-sensor plan.

This works, provided the combination groupid - startdate is unique:

SELECT s1.groupid, s1.id FROM schedule s1, (
  SELECT groupid, MAX(startdate) startdate
  FROM schedule
  WHERE @date >= startdate
  GROUP BY groupid
) s2
WHERE s1.groupid = s2.groupid
AND s1.startdate = s2.startdate