Sorry..R2 didn't have a piece of the map, he had the whole map. The story goes that R2 got the map , lets say it's a map containing the location of every jedi temple ever known to the empire,whilst downloading information aboard the death star. He is then able to cross reference that with the piece from Lor San Tekka to find Luke's location.
Where is this stated? Cuz it's not in TFA.
EP7 shows R2 literally waking up and projecting a map with a hole in it. BB-8 then completes it and they find Luke's location.
He didn't cross reference, he literally completed the map with the missing piece.
"LARGE NAVIGATIONAL MAP WITH A SPECIFIC MISSING CHUNK!"
From the script itself