Optimising this very slow MySQL Query - mysql

Question

I'm not particularly knowledgeable about MYSQL queries and optimising them, so I require a bit of help on this one. I'm checking a table of international cities to find the 10 nearest cities based on the longitude and latitude values in the table.
The query I'm using for this is as follows:
SELECT City as city,
SQRT(POW(69.1 * (Latitude - 51.5073509), 2) +
POW(69.1 * (-0.1277583 - Longitude) * COS(Latitude / 57.3), 2)) AS distance
from `cities`
group by `City`
having distance < 50
order by `distance` asc
limit 10
(The longitude & latitude values are obviously placed dynamically in my code)
sometimes this can take around 3-4 mintues of my development environment to complete.
Have I made any classic mistakes here, or is there a much better query I should be using to retrieve this data?
Any help woould be greatly appreciated.

Answer 1

Assuming City is unique and you are abusing GROUP BY and HAVING in order to get a cleaner code
SELECT City as city,
SQRT(POW(69.1 * (Latitude - 51.5073509), 2) +
POW(69.1 * (-0.1277583 - Longitude) * COS(Latitude / 57.3), 2)) AS distance
from `cities`
where SQRT(POW(69.1 * (Latitude - 51.5073509), 2) +
POW(69.1 * (-0.1277583 - Longitude) * COS(Latitude / 57.3), 2)) < 50
order by `distance` asc
limit 10
If City is unique then the aggregation is done on single rows.
MySQL uses sort operation to implement GROUP BY.
Sort complexity is O(n*log(n)), so without indexes this is going to complexity of GROUP BY.
If City is not unique than the filtering in the HAVING CLAUSE is done on one arbitrary row which is for sure not what the OP intended.
The case where HAVING and WHERE are both relevant for filtering and HAVING has an performance advantage is where the filtering is done on the aggregated column, there are some heavy calculations and the GROUP BY operation significantly reduce the number of rows
select x,... from ... group by x having ... some heavy calculations on x ...