For geocoding we are using the Nominatim
from the below URL http://nominatim.openstreetmap.org/ But i need to implement suggestion on the address, do OSM has this service like Google and ESRI
is their any other method to implement?
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No, currently Nominatim doesn't support suggestions but this feature is on the todo list. As Nominatim is open source you are welcome to help implementing it.
i have found a little similar to the suggestions
from geoName server which is open data
By changing the style=SHORT parameter we can just get the names with lat long
more on Geoname server here