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I need to develop a solution that will provide the ability for a user to search based on a city and state. The user should have the ability to request that the search results include not just matches for that city and state, but also include matches in a 25, 50, 100 mile radius. I see that job sites do this type of thing. How is this done and are there vendors that provide open API's for it?

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It seems that what you're looking for is a GIS (Geographical Information System) in which each (or some) piece of information is linked to its geographical location. Such sistems allow to perform spatial searches on those geographical location, eg. "give me all stores in a 5 mile radious from this position which sells a specific product" (combining spatial and traditional searches is also possible).

Now some examples of technologies you can use:

  1. PostgreSQL + Postgis: This opensource combination of database and geographical extension is powerful enough for most of basic user needs. You can start from here
  2. MySql Spatial
  3. Oracle Spatial
  4. ArcSde (ESRI)

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