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I would like to find out how I can perform a distance measurement between 2 known points along a street network, similar to the way google maps gives directions and distances. Is this possible in CartoDB?

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CartoDB doesn't have routing capabilities, so unless you have a dataset with the streets and you play with geospatial queries on them, this is not a built-in feature.

If you have the streets dataset, you could probably split them in different segments and try to build an algorithm with PostGIS to get the minimum distance path by adding the sum of each segment, but take into account that routing information like for example the directions of the streets, or the amount of traffic that each street segment is suffering is something out of the scope.

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