Geospatial search: varying radius receptors and fixed event point

Therms of the problem:

• given a certain point on the Earth we will call "event point"
• given a certain number of other points on the Earth, we will call "receptors"
• given that any receptor has a circular area around it, with a variable radius we will call "reception area"
• given that the radius of the reception area can vary in a set of discrete sizes [1,10,20,50,100,200] miles

I want to calculate in linear time all the receptors having a reception area which includes the event point.

Since clustering seems a solution, I would to like to know how various solution like, MongoDB GeoSpatial, Postgres GIS, MySQL Geospatial and other DBMS handle this problem.

Do them use clustering internally?

In any case: Which is the best "out of the box" solution for this problem?

The answer to your 'what is the best solution?' question is "It depends".

For SQL Server, a good overview of the spatial data features is https://msdn.microsoft.com/en-us/library/bb933790.aspx

And relevant to your question is spatial indexes: https://msdn.microsoft.com/en-us/library/bb895265.aspx

For the example given, a rough idea is to store a geography type for your Receptors and EventPoint then use the STContains function in the where clause. https://msdn.microsoft.com/en-us/library/ff929274.aspx

Some pseudo-SQL might be:

DECLARE EventPoint Geography = ...
SELECT * FROM Receptors R WHERE R.Receptor.STContains(EventPoint)

Hope this is of use.